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Erm. If it's melting the rock around it, then the rock is your cold sink. By the time the temperature of the rock catches up with the probe, it's already molten anyway.



More specifically: the interior of the probe is 2000F, the surrounding rock melts at 1000F. That's a pretty good temperature gradient right there.


The rock would not work as a cold sink - the cold rock is too far from the probe. The rock right near the probe is at almost the exact same temperature.


And that's exactly why the probe will take 30 years to move 100km. It's going to be a very slow process.




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