Why doesnt mankind "collect" thermal energy (there has to be some way: thermal couplings, detour over chemical energy, whatever) and after it has been concentrated at one point, turn it to electrical energy (like steam turbines do) or at least radiate it to space?
Collecting thermal energy is really hard. As others have said, things like heat pumps exist for moving heat around, but the laws of thermodynamics (which are fairly fundemantal in physics) require that moving heat around will always generate more heat.
Now, the amount of extra heat generated can be less than the amount of heat that's being moved - so if we had a way to build a heat pump that moved heat out of the earth system and into space, then it might be worthwhile. There are three problems with that,
We don't know how to do that. A system of pipes going into orbit probably isn't practical!
Having got the heat into orbit, getting it away from the equipment and into space is hard. You've probably learned about heat moving by conduction, convection, and radiation? The first two are not available in space, because there's no material to conduct into and no atmosphere to convect. So radiation is all that's left. On top of the hypothetical heat pump to orbit, we'd need a massive radiator system in orbit as well.
The scale at which it would have to be done is gigantic. Even if we knew how to do it, we might not be able to do it.
So it probably isn't theoretically impossible - at least so far as we know - but it's not something that's possible at the moment.
It's also worth noting that like all ideas that are about getting rid of heat rather than reducing the greenhouse effect, it doesn't actually solve the problem - it just mitigates the symptom. If we carried on emitting greenhouse gases while using this system then we'd have to keep using this system, more and more, for ever.
(theoreticians: am I missing something? Is there actually a theoretical, rather than practical, blocker here?)
Your middle school physics perhaps hasn't gotten to thermodynamics yet. The three laws of which can be summarized as 1) You can't win; 2) You can't even break even; 3) You can't leave the game.
The crucial point here is that heat engines don't actually work on heat, they work on temperature differences. So you can't really "collect" heat and turn it into other forms of energy, because you need a colder place to transfer the heat to in order to convert the heat to say electricity. Which is why power plants are usually situated by oceans, lakes, or rivers, in order to use the water as the cold side of the generator. (And ones that aren't have large cooling towers, in order to use the air.)
When you do move heat around, say with the heat pumps used for home heating and cooling, you're always using some extra energy to "pump" the heat from one place or another. If you're heating, you move some heat from the ground outside to your house, but the net result is that the system of ground+house gets a bit warmer, because the electricity used for the pump becomes heat.
WRT sending the heat back into space, that's actually the cause of global warming. Atmospheric CO2 acts as an insulating blanket, preventing some of the sun's heat from being radiated back out into space. By increasing the amount of CO2 in the atmosphere, we've increased the thickness of the blanket, so the Earth gets warmer.
The new materials reflect a broad spectrum of light, in much the same way as mirrors or white paint do. In the crucial 8–13-µm part of the infrared spectrum, however, they strongly absorb and then emit radiation. When the materials point at the sky, the infrared rays can pass straight through the atmosphere and into space. That effectively links the materials to an inexhaustible heat sink, into which they can keep dumping heat without it coming back. As a result, they can radiate away enough heat to consistently stay a few degrees cooler than surrounding air; research suggests that temperature differences could exceed 10°C in hot, dry places.
As others have pointed out, if you use the energy, it turns right back into heat.
Radiating it back to space is at least theoretically possible. But there is a problem with scale.
The Earth receives about a 100 petawatts of energy from the sun. And it radiates almost exactly the same amount back out.
Everything humanity do with energy is about 0.02 petawatts. Even if we radiated all that energy into space it still wouldn't matter much.
Still, it is barely possible to do something like this, by bouncing the sun's light off the Earth surface as it arrives. While mirrors would be ideal for this job, they are expensive. Fortunately, any really bright white object does almost as good a job. Look up Albedo for more information.
It would take a very large area of land to make any difference. And land is expensive. And we would need a lot of white stuff to do the job. Even if it is cheap by the square meter (sq feet), it will be expensive by the million square kilometer (million sq mile).
So, this is on the list of things we could do if we only found the money for it.
Just to hammer it down: the amount of energy transferred to Earth by the sun every single day is colossal. In comparison, the heat generated by all human activities is negligible.
For instance, burning every single tree on Earth would release less than 1% of the heat the sun sends our way every day!
Taking human activities as an intuitive reference point is utterly misleading. Heat exchanges in the atmosphere involve massive amounts of energy that are far beyond anything human industrial capabilities can handle.
Greenhouse gases act like a kind of space blanket: a very thin and light insulating layer that can still trap quite a lot of heat.
Though the excess of gases we release only capture a tiny extra fraction of it (well below 1%), the energy the sun sends our way is so tremendous that this little extra heat is enough to mess up our climate badly.
Our problem is not to make any use of this extra solar energy. We could move around a minute fraction of it to our advantage (for instance concentrating it inside a house in winter and pumping it out in summer), but as a global system our habitat (the surface of the Earth and a bit of breathable atmosphere above) is receiving far, far too much heat, on a scale that dwarves all human uses of energy.
Our problem is to get rid of it, that means sending it some place where it can't wreak havoc with our climate. At this scale, that leaves only outer space or deep soil as potential dumps.
So far our atmosphere did quite a nice job of sending solar energy back into space, but we fouled it up. What a bummer...
We sure could think of just moving all that heat out of the way ourselves. But alas, as the 2nd law of thermodynamics and its dreaded entropy states, any kind of mechanical work requires additional energy and generates more heat. Even a refrigerator adds more heat into the environment than it pumps out of its internal compartment. All we can hope to achieve is transfer heat from place to place. At the cost of more energy, raw materials, time, industrial capacity and, naturally, money.
That is dictated by fundamental laws of physics that no amount of wishful thinking can sway.
Painting deserts white or drilling deep underground geothermal wells or putting fancy space radiators into orbit are just sci-fi fantasies.
We simply don't even come close to having the energy, materials and technology to implement any of these on a scale that would solve the problem.
Picture yourself being wrapped in a space blanket, getting a bit too hot for comfort. Trying to move the hot air away from your body will only make you warmer, while removing the blanket might cool you down fast, with a lot less efforts.
Indeed, the only thing we could hope to act upon is the blanket itself.
Wisdom would dictate to start by not making it any thicker. Stop burning fossil fuels and breeding farting cattle for a couple of centuries, waiting for all the junk we spewed so far to dissipate.
There is also the crackpot scientist alternative: spewing more junk (like sulphur) into the atmosphere to try and mitigate the greenhouse effect. Frankly I hope I'll be dead before I see the idiots try.
Your idea: concentrating the heat, using the energy for something useful and then dissipating it into space could actually be accomplished by a space mirror.
There is a special orbit called L1 that's in between the Earth and the Sun and is just the right distance so that something in that orbit will track and orbit in sync with the Earth. It could both shade the Earth a bit and be a massive power plant.
You might check out this article from live science on space mirrors. It goes over the pros and cons of this idea.
Wikipedia also has an entry on this idea.
Of all the types of energy there is, heat is the "waste" of the energies. See, energy is only useful if organized, and heat is the least organized of them all. I.e, the energy must be able to push car wheel in that particular direction, not to every direction at random, like molecules of a hot gas would.
In order to reorganize the energy, according to the laws of physics (the second law of thermodynamics, in particular), you must have a cold place to where the heat could flow. Most (all?) heat engines relies on the environment being colder than the heat source in order for it to work: a car or a airplane engine only works because the ambient temperature is smaller than the temperature inside the engine, and a coal plant relies on the ambient being cooler than the steam turning the turbines.
By being immersed in a hot ambient, you can't use that very ambient as the cold side in order to extract energy from it, so you can't possibly build a device that is powered solely on the heat of the environment it is immersed in.
That is one half of the problem. The other is: if we could extract energy from the environmental temperature, we would certainly not radiate it away to space: we would use it as electricity, power our cars, planes, and would never need fossil fuels again.
Fossil fuel based energy is very inefficient; the amount of heat wasted exceeds that which gets used. In addition global heating from enhanced greenhouse effect is adding heat at rates estimated at around 100 times that from total waste heat. In order to get zero global heating (whilst continuing to burn fossil fuels) by collecting heat and sending it to space requires collecting in excess of a hundred times more energy than human economies are currently using as well as developing and building and operating the technology to send all that heat somewhere else, ie to space.
That is effectively impossible, but developing a means to utilise low grade heat for energy generation could significantly aid the displacement fossil fuel burning, that would reduce global heating by that factor of a hundred. Technology for turning low grade heat into higher grade energy exists - eg Stirling engines - but they are not cost effective. Some other tantalising possibilities do exist, such as Nantennas aka Optical Rectennas.
However, effective low emissions energy options that reduce fossil fuel use and the enhanced greenhouse warming and that are cost effective already exist; I think those should be the primary focus of our current response to global warming.
The problem with turning many forms of waste heat into other forms of energy by conventional (heat engine) methods is that significant temperature differences are needed - and that the temperatures making up the differences are counted from absolute zero (0 Kelvin). Only if that ratio is large, you get an efficient conversion. For example, if you look at the waste heat from a computer CPU, it might be at 340 Kelvin, 40 degrees Kelvin (Kelvins are absolute-zero-referenced centigrades for you Fahrenheit types) over an ambient temperature of, 300 Kelvin. You can't force the heat to build up to much higher levels since you will damage the CPU. The efficiency of a heat engine trying to make anything useful of this situation would be 40K/340K*100% = drumroll ... 11%. Hardly WORTH trying to recover.
This is because Carnot, one of the patron bastards of physics, made that the law in 1824, and no one repealed it yet.
This does not apply to heat radiation, which isn't heat per se but heat that has already been converted into long wave infrared light, which gets converted back into heat if it hits something. It can indeed be relayed at will by lenses, mirrors and prisms made of the appropriate materials (not: run of the mill window or optical glass!). Unfortunately, creating significant heat radiation is also something that takes high temperatures....
Well the most straight forward way to radiate sunlight into space is with a mirror.
But creating millions of square miles worth of mirrors sounds very expensive. Probably in the range of a 100s of Trillions of US dollars. If we got rid of all government spending we might be able to pay for it over the course of a 100 years or so.
Mankind does collect natural sources of heat and turn it into useful energy: heat pumps, solar arrays, geothermal etc, but it would be impossible to reduce global warming in this way. Most of the heat collected for useful purposes is in any case given back to the atmosphere when the energy is used. If you think about it, even wind farms are collecting solar energy, because it is the sun's heat which drives the winds. When the energy is used, it is re-converted into heat. As a physics student you should know this.