maybe not so hot indeed due to the scarce air that's why it's so cold at night on the moon. Only turn on the reactor at night to generation and use capacitors at day?
You can't really turn fission reactors on and off, they're always producing decay heat even if not being used for power generation. But why not radiate the excess heat into the crust of the moon with a subsurface loop, kind of like a ground source heat pump.