Under the layer of regolith, Moon crust is mostly basalt ([1]), which has about 1.6 W/mK thermal conductivity ([2]). Not great, not terrible.

We all know how cold it is to stand on a stone floor - unlike wood or plastics, it keeps sucking that heat off.

1. https://en.wikipedia.org/wiki/Internal_structure_of_the_Moon

2. https://en.wikipedia.org/wiki/List_of_thermal_conductivities

Nice Chernobyl reference!

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Thanks! I now get the reference, although it was completely accidental. I should watch the movie, I guess.

It is a miniseries and it is excellent and gripping from start to end.

Your forgetting about radiation. You don't need to conduct it all away, there are 3 modes of heat transfer, conduction, convection and radiation. In this case it's the radiation they'd rely on.

Sunlit surface of the Moon can reach 127 C. Don't know what type of reactor they choose, but it obviously won't work for boiling type of reactors.

UPDATE: I forgot about not-water coolants. Molten salt or liquid metal reactors can work at 500 C, so would radiate anyway, right.

Radiation doesn't need a temperature gradient anyway