From https://phys.org/news/2006-03-probing-earth-core.htmlt: the vast majority of the heat in Earth's interior—up to 90 percent—is fueled by the decaying of radioactive isotopes like Potassium 40, Uranium 238, 235, and Thorium 232 contained within the mantle. These isotopes radiate heat as they shed excess energy and move toward stability. "The amount of heat caused by this radiation is almost the same as the total heat measured emanating from the Earth."

Id say based off this, tapping into the heat to draw power is not going to cause any cooling effect of the earths interior.

Its also cooling albeit very slowly on its own regardless.