... causing it to cool down?

This answer to the question 'Why has Earth's core not become solid?' over on Physics seems to claim the answer is no.

The core is heated by radioactive decays of Uranium-238, Uranium-235, Thorium-232, and Potassium-40, all of which have half-lives of greater than 700 million years (up to about 14 billion years for Thorium).

The core isn't hot just because of remnant heat left over from formation, the heat energy in the core is continually renewed by radioactive processes.

If so, would it result in an ice age?

This energy from the core must already be continually dissipated up through the mantle, through the crust, into the atmosphere and eventually into space (or else the planet would be heating up).

All we could possibly do is speed the dissipation of this energy through the crust, any energy we extract would get to the surface anyway.

As others have pointed out geothermal energy is a tiny fraction of what heats our atmosphere, most of that comes from the sun.

Even if this were not the case, for us to cause an ice age, would require us to have near complete control over geothermal release through artificial means. We would have to extract enough energy over a long enough period from deep enough in the earth that there was no longer significant natural heat dispersion through the crust. Then we would have to stop and bottle up our manual extraction so that the heat had no other means to escape but rising through the crust in the natural way. The heat present in the atmosphere would dissipate into space far quicker than new heat would rise through the crust.

I imagine both the process of our intervening to the point of control, and our sudden relinquishing control would both have significant effects aside from climate change: earthquakes, volcanic eruptions, disrupting continental drift...

If not, how does it retain its heat?

I hope it is clear that it doesn't.

... causing it to cool down?

This answer to the question 'Why has Earth's core not become solid?' over on Physics seems to claim the answer is no.

The core is heated by radioactive decays of Uranium-238, Uranium-235, Thorium-232, and Potassium-40, all of which have half-lives of greater than 700 million years (up to about 14 billion years for Thorium).

The core isn't hot just because of remnant heat left over from formation, the heat energy in the core is continually renewed by radioactive processes.

If so, would it result in an ice age?

This energy from the core must already be continually dissipated up through the mantle, through the crust, into the atmosphere and eventually into space (or else the planet would be heating up).

All we could possibly do is speed the dissipation of this energy through the crust, any energy we extract would get to the surface anyway.

As others have pointed out geothermal energy is a tiny fraction of what heats our atmosphere, most of that comes from the sun.

Even if this were not the case, for us to cause an ice age, would require us to have near complete control over geothermal release through artificial means. We would have to extract enough energy over a long enough period from deep enough in the earth that there was no longer significant natural heat dispersion through the crust. Then we would have to stop and bottle up our manual extraction so that the heat had no other means to escape but rising through the crust in the natural way. The heat present in the atmosphere would dissipate into space far quicker than new heat would rise through the crust.

I imagine both the process of our intervening to the point of control, and our sudden relinquishing control would both have significant effects aside from climate change: earthquakes, volcanic eruptions, disrupting continental drift...

If not, how does it retain its heat?

I hope it is clear that it doesn't.

... causing it to cool down?

This answer to the question 'Why has Earth's core not become solid?' over on Physics seems to claim the answer is no.

The core is heated by radioactive decays of Uranium-238, Uranium-235, Thorium-232, and Potassium-40, all of which have half-lives of greater than 700 million years (up to about 14 billion years for Thorium).

The core isn't hot just because of remnant heat left over from formation, the heat energy in the core is continually renewed by radioactive processes.

If so, would it result in an ice age?

This energy from the core must already be continually dissipated up through the mantel, through the crust, into the atmosphere and eventually into space (or else the planet would be heating up).

All we could possibly do is speed the dissipation of this energy through the crust, any energy we extract would get to the surface anyway. As others have pointed out geothermal energy is a tiny fraction of what heats our atmosphere, most of that comes from the sun. Even if this were not the case, for us to cause an ice age, would require us to have near complete control over geothermal release through artificial means. We would have to extract enough energy over a long enough period from deep enough in the earth that there was no longer significant natural heat dispersion through the crust. Then we would have to stop and bottle up our manual extraction so that the heat had no other means to escape but rising through the crust in the natural way. The heat present in the atmosphere would dissipate into space far quicker than new heat would rise through the crust.

I imagine both the process of our intervening to the point of control, and our sudden relinquishing control would both have significant effects aside from climate change: earthquakes, volcanic eruptions, disrupting continental drift...

If not, how does it retain its heat?

I hope it is clear that it doesn't.

... causing it to cool down?

This answer to the question 'Why has Earth's core not become solid?' over on Physics seems to claim the answer is no.

The core is heated by radioactive decays of Uranium-238, Uranium-235, Thorium-232, and Potassium-40, all of which have half-lives of greater than 700 million years (up to about 14 billion years for Thorium).

The core isn't hot just because of remnant heat left over from formation, the heat energy in the core is continually renewed by radioactive processes.

If so, would it result in an ice age?

This energy from the core must already be continually dissipated up through the mantle, through the crust, into the atmosphere and eventually into space (or else the planet would be heating up).

All we could possibly do is speed the dissipation of this energy through the crust, any energy we extract would get to the surface anyway.

As others have pointed out geothermal energy is a tiny fraction of what heats our atmosphere, most of that comes from the sun.

Even if this were not the case, for us to cause an ice age, would require us to have near complete control over geothermal release through artificial means. We would have to extract enough energy over a long enough period from deep enough in the earth that there was no longer significant natural heat dispersion through the crust. Then we would have to stop and bottle up our manual extraction so that the heat had no other means to escape but rising through the crust in the natural way. The heat present in the atmosphere would dissipate into space far quicker than new heat would rise through the crust.

I imagine both the process of our intervening to the point of control, and our sudden relinquishing control would both have significant effects aside from climate change: earthquakes, volcanic eruptions, disrupting continental drift...

If not, how does it retain its heat?

I hope it is clear that it doesn't.