NASA wants nuclear reactor on the Moon by 2030

“NASA believes it will need 40 kilowatts of power for the first lunar inhabitants”

Sounds like it’ll only need to be a small reactor, something akin to what goes in a submarine. I’m no expert but presumably something like that is significantly quicker and easier to build than a megawatt scale nuclear reactor. The obvious challenge that the bidding companies will have to solve in the next 8 years is how to get the materials into space safely and assemble them on the moon.

While the temperature is rather wide, I would expect the actual energy difference to be relatively small, as without atmosphere for convection and little conduction down due to the insulating properties of regolith it may end up heating just the very surface, so very little mass.

The fact that people could stand in spacesuits on the surface for significant amounts of time, with little heat removal capacity, likely means the actual energy insolation isn't huge. Functionally it'll be the same as on earth at a similar angle to the sun, minus atmospheric absorption (which a quick google says may be in the order of 20%).

Similarly you need a way of easily removing the heat from the "cold" end of whatever system you use to generate power, as otherwise it'll quickly heat up and remove the differential. Again without convection you'll likely rely on radiation, which may not be a big difference at the temperatures we're looking at, and conduction through the ground, which may require some way of sinking significant heat into the ground. Possibly using some pipes driven deep containing some kind of heat transporting medium, e.g. a liquid, but then you have issues on finding something with a high heat capacity that doesn't vaporize/solidify at any of the temperatures.

The moon rotates once per month, so nights are about 2 weeks long.

Continuous solar power might be possible with a ring of panels around the south pole.