There's a sibling comment asking for a source, which I can't reply to for some reason.

I can't speak to the receding magma or facilities damage, but "proportional to the cross-section of the borehole" is just like first year thermodynamics. If someone has more familiarity with electricity (I guess common on HN?), here's a reasonable introduction to the comparison to circuitry: https://lpsa.swarthmore.edu/Systems/Thermal/SysThermalElem.h...