Its normally said that deserts cool planets because they reflect more radiation back to space. According to this logic if all the land mass in the world was desert the world should be colder. Is it true that the average temperature of a desert is higher than green land in a similar climate? If so wouldnt the average surface temperature be higher if all the world was a desert? And if so how can we still claim deserts cool the earth? Isnt the metric of whether we have global warming, the average surface temperature?
Water vapor is a powerful greenhouse gas. The key characteristic of a desert is lack of precipitation, and that is typically correlated with a low humidity. That reduced humidity means more thermal infrared radiation going from the Earth's surface to space.
Desert doesn't necessarily mean hot. A place is qualified as a desert if it has very reduced precipitation. The Atacama Desert, one of the (if not the) driest places on the planet, can get quite cold. Almost all of Antarctica is technically a desert, and it is very cold. At the height of the last glaciation, much of the northern portion of the Northern Hemisphere was technically a desert, and it too was very cold.
On the flip side, a billion years or so from now, the Earth is predicted to go through a warm greenhouse phase due to the Sun getting more luminous. The oceans will evaporate, some water will be split into hydrogen and oxygen, and eventually the hydrogen will escape into space. At that point, the entire Earth will technically be a desert as there will be no water anywhere, and it probably will be hot.
Blisteringly hot at day, freezing cold at night
Assuming that "deserts" here mean sandy places with extremely dry air, then it will get really hot at day, but freeze over at night.
Deserts, which are mostly made up of sand (excluding a few places of bare rock and stuff), tend to act like mirrors. Sand has an extremely low specific heat capacity i.e. it heats up quickly with much less energy, but also cools down really quickly. Sand also has a really high albedo i.e. it is very reflective, so it tends to reflect away sunlight. Dry sand also has the nasty habit of reflecting away infrared (wet sand, on the other hand absorbs IR). This gets even worse, as desert air is generally extremely dry, with no water. If it had been humid air, there would atleast have been a chance of water absorbing this heat and thus reducing the temperature (Water has a extremely high specific heat, second to only hydrogen). But with no water vapour, there is nothing to absorb the heat.
Assuming that we switched Earth's entire surface with just sand and a few areas of exposed rock, Earth would look like Mercury on steroids. The dayside would get ridiculously hot, perhaps hundreds of degrees, as the sand reflects infrared and visible light back into the air, heating it up rapidly. However, since sand has an extremely low specific heat capacity, it will rapidly cool, once daytime has ended. At night, the temperatures may plummet to below freezing, as the sand quickly releases its heat away.
TlDr Blisteringly hot at day, but freezing cold at night