Is heat a renewable resource

It depends on what fuel is used.

If the fuel is coal, natural gas, gasoline, or oil, then it is not renewable because no one makes these things.

If the fuel is a biomass such as wood, it might be renewable or not, depending on whether it is regrown. Wood that is responsibly cut comes from trees or forests that continue to grow, and these take carbon dioxide out of the air, offsetting the fact that the fire burning the wood puts carbon dioxide into the air.

Other examples can be cited, but the answer to the question lies in whether the fuel is grown or made currently, or does it come from some old repository, usually underground.