Indeed, all energy sources are of finite supply, but its a question of scale. There's a finite amount of fossil fuels, the sun only puts on a finite amount of light and the lifetime of the Sun is limited, and there is a finite amount of trapped heat inside of the Earth. In fact, there is a finite amount of hydrogen available in the universe with which to form stars. But we as a species are trying to maintain our style/standard of living out as far as possible - currently, our efforts are at extending our society beyond the availability of fossil fuels. One day, hopefully, we will be trying to extend our society beyond the life of the Sun. The issue now, is how do we get beyond fossil fuels?
The ultimate energy source, for which we all hope, is to master controlled fusion. We're not there yet. So we look to other sources to fill the need as fossil fuel supply dwindles. Together, solar, wind and geothermal may be able to bridge the gap. If, as some suggest, fusion will forever be illusive, then I'm afraid we're already screwed.
As to your question, IIRC, at current consumption rates, we would barely make a dent into the stored heat inside the Earth; however, you are correct, if we continue to grow consumption and suck heat out indefinitely, it will eventually make a difference, but that is hopefully far enough out into the future that it permits us to perfect fusion.