Will geothermal cooling be greatly affected by global warming?
I presume that by geothermal cooling you mean geothermal energy. Yes, it's an attractive option and is used a lot in Iceland, but unfortunately there are not many places that have such easy access to it as Iceland. Geothermal energy will be just one source of non-polluting energy, along with hydro-electricity and many others. Today's global warming is just a passing phase, and will be followed sooner or later by another ice age.

The Earth is gradually cooling as geothermal heat is lost into space and the crust is getting thicker, as has already happened on Mars, but this will have no noticeable effect on Earth for many millions of years, by which time we will have gone to join the dinosaurs.