[Retric]

> isn't there a finite amount of heat under Earth's crust?

We can't make meaningful change over the next million years which is vastly past any reasonable projections.

The earth is 6 * 10 ^ 24 kilograms. Changing that much mass by 1 degree would take ~2000 Joules * 6 * 10 ^ 24 kilograms, but we don't get 100% efficiency so let's say it's 10% for a nice low estimate to get 1.2e + 27J.

Worldwide energy use is 5.67 × 10^20J / year. So circa 2 million years of total worldwide energy supply for a 1 degree change. Of course it's not a static value as nuclear reactions and tidal friction are also adding energy, while energy also slowly escapes though the crust.

[cmbuck]

Thank you for this analysis. A 1 degree change over 2 million years strikes me as rather unlikely to meaningfully affect magma currents

[astrodust]

The movie The Core, like so many others, are only plausible if your math is really, really wrong.