[jandrese]

I have always assumed that the first moon colony would be on the north or south pole to avoid this issue. Not too hard to imagine a solar array set up to track the sun with a very slow rotation. The colony itself would be in a crater to avoid direct sunlight and provide a place to dump the heat from the solar array.

Otherwise the need to bring enormous power storage to handle the half month of darkness and bitter cold makes solar a bit impractical and the only other reasonable alternative is nuclear power.

The big problem with attempting to exploit the temperature differential is that it happens on such a slow cycle that the total amount of energy available is quite low.

[BurningFrog]

Could you exploit the temperature differentials between the either hot or cold surface, and the presumably in-between temperature at the bottom of a drill hole?

[jandrese]

In theory the temperature underground should be the average of the surface temperature, so you could use that gradient to generate energy at night. Someone smarter than me would have to do the math on the energy density of a scheme like this, my gut says it's going to be fairly low and you will need a really big power plant to supply even a modest colony.