Also, nuclear power plants are steam powered. Good luck. They /might/ drop a nuclear battery, like the kind in some old satellites or apace probes, on the moon, generating a couple hundred watts with 1970s technology.

On the moon isn't really "in space" in terms of temperature distribution because the heat actually has somewhere to go, the moon.

Would only be cool enough at night though.

So... The US has plans to build nuclear generators on the moon too, kilopower has been an ongoing project for the past decade and I have no doubt we'll be ready to deploy one of these reactors as soon as we start building infrastructure on the moon again in the near future.

Nuclear power is not new for space, it's an obvious choice, one of only two choices in fact. And for what it's worth, Russia/USSR has had far more nuclear powered space probes over the years than the US has, so this isn't exactly new for them either.

As for cooling, yeah, if you generate power you need to dissipate that heat. Your generator will put out heat which needs to be dealt with and then using that electricity will also generate heat which needs to be dissipated. That said, one kind of power is not harder than another, dissipating a megawatt of solar power is just as complicated as a megawatt of nuclear. So the real question is: how much power do you need? The complexity of the project will scale relative to that.

All in all, we've used nuclear power in space before and we will need to do it again, radiators are not all that hard.