SpaceX offers details on orbital data center satellites
spacenews.com
spacenews.com
I'm sure they can manage heat issues so long as the scale of these satellites are very modest.
If instead you picture a satellite with some compute modules in it you’re good. Can a satellite generate power? (Yes) can a satellite scrub heat equal to the amount it can generate with solar panels? (I don’t know, ask someone who has done it successfully a few times)