If it's that simple, then it should be pretty easy to show mathematic proof.
We already have relatively low power devices that essentially cool via IR radiation.
But don't bother, because you've already lost the argument: As with all things SpaceX that people claim are impossible until SpaceX actually pulls it off (and has over a dozen times now) they're talking about whether it's cost effective, not whether the physics works.
SpaceX is not rewriting the rules of physics. They are rewriting the rules of engineering.
No competent person is arguing that it can't physically work.
Actually highly competent people are arguing against space based data centers as an alternative to ground based. There will be AI processing in orbit, but it will generally be for local in orbit needs.
SpaceX has done this so many times with so many things ...
Getting reusable rockets to land on their tail, turning the decades old sci-fi into reality, was a matter of engineering. The difficulty of cooling in space is a matter of physics.
that you'd figure people would learn by now to make arguments based on cost effectiveness. Yet here you are, no mention of cost effectiveness anywhere.
SpaceX's cost effectiveness is largely through reusability. Again, an engineering based solution. If and when we engineer AI processors that do not generate much heat, they will be easier to build and locate on earth. AI in orbit will largely remain for orbital needs, not ground based needs.