Okay, so you admit it is possible. Cooling is not the problem. We're making progress.
Now your argument is that it's unprofitable. Here's the calculator: https://andrewmccalip.com/space-datacenters
Specifically, if SpaceX can get the price of a satellite down to $8 per watt (about $2 million USD) then it will compete with terrestrial.
I just don't understand how you can be so certain that they can't do that. I'm not certain that they can, but being certain that it's impossible seems completely evidence-free.
This calcualtor is bullshit (inflated terrestrial costs and underflated orbital costs). It doesn't pass the basic sniff test: $15B for 1GW of terrestrial power is more than enough to build AN ENTIRE 3GWe NUCLEAR POWER PLANT. From scratch. With 75 years of expected life.
So no, the calculations show that space is NOT feasible unless you want to do that for nefarious reasons: evading regulations, using AI for criminal enterprises, military use, that sort of thing.
Only these applications have the profit margin that even comes close to justifying it.