A geothermal plant running on full capacity may deplete its geothermal well in 50 years. It may take 1000 years before the geothermal system becomes a resource again [1]. Is that human timescale?
Well that's an interesting question, the short answer is it's shining anyway and hitting the surface regardless, might as well use it. The long answer is only so much is hitting the surface and you have to raze living areas that need it to use it so you still have to be cautious and selective.
Geothermal is radiating into space from the center and is residual energy from formation and from the decay of radioactive material inside. If it is used that increases the rate at which it radiates, and too much of that has terrible potential implications, such as slowing of tectonics and lowering of the magnetic field. It may be hard to see humans using enough to do this, but someone could've said the same about fossil fuels when they began being used. This is not so with the sun, which is radiating the same regardless.
