Very astute analysis! LOL.
Al Gore said last month that the center of the earth is several million degrees and all we have to do is dig a few holes a couple miles deep to get unlimited free energy.
With Al’s luck he would hit oil first.
Miniature Stirling engines have numerous applications. Large scale Stirling engines probably have no more utility than large breasts on a boar/
The big problem is cutting holes in the rock (it's very hard and very acidic, and therefore corrosive).
In many places you only need to drill 100 feet or so.
In Southern Indiana and in much of Kentucky it is a common practice to stick one end of a heat pump system into a cave. Where the caves are filled with sand you just dig a borehole and plant an "immersion" system in to work as your heat sink. Now that doesn't give you free energy, but it gives you exceedingly inexpensive heating and air conditioning.