Sure, once you have two-week power-storage infrastructure. (And the scale to harvest a useful amount of energy once a month on average.) In the meantime, i.e. our lifetimes, you have countries that can build space nuclear reactors and countries being performative.
Beyond all this, I meant novel when I said novel. The regular extremes of heat and cold offer all sorts of interesting ideas. You've got room for predictable and endless convection on basically an arbitrarily large scale there. There is certainly going to be some clever way to exploit this in a novel fashion.
[1] - https://en.wikipedia.org/wiki/Radioisotope_thermoelectric_ge...
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.
1. Batteries are heavy, and space ain't cheap. Current launch pricing is about $1.5k/kg to LEO. The Moon will be more, it's further away. Even if Starship brings that down by a factor of 10, transportations costs are still going to be astronomical.
2. The day-night cycle on the Moon is slow. Your batteries are going to need to be able to store half a month worth of power. You'll need 15x more batteries on the Moon than you would on Earth.
