> On the moon you have no atmosphere to do it with radiators with fans, so I gues you would have to make huge radiators which simply emit the heat away as infrared radiation?

Exactly. You can still transport the heat efficiently away from the computer using heat exchangers with some medium, but in the end radiators with a large enough surface area will be required.

Works well enough on the ISS, so I imagine it'd work just as well on the Moon.