Seems to me that for half the synodic period (avg ~ 29.5 days) one could store heat in some medium, and for the other half, store “cold” in some medium, and then use those media to run a heat exchange engine, with the temperature difference between lunar day and night averaging around 500 degrees F.
Carnot and Sterling on the moon. Next on Oprah.
Good idea. Lots of options. I don’t think energy supply will be much a problem.