[dpark]

Then nothing is renewable. Eventually the sun runs out of fuel.

Renewable cannot be taken to mean truly limitless or nothing is renewable. Renewable means practically limitless. How much heat do we have to pull from the Earth before it causes a problem? I don't know, but I bet it's a lot more than we will in the next 10K years even with heavy investment in geothermal.

The Earth also doesn't have a fixed amount of heat inside. Heat is constantly being produced by, e.g., tidal forces and radioactive decay.