If you solve your cooling problem in space by distributing 10000 servers across 100 orbits then you replace one engineering challenge with the next; good luck with the satellite-satellite optical crossbars, and even more with the time travel beam shapers to get the communication latency between the components of your "orbit-distributed data center" to-target.
(the sarcasm is intended; there are some usecases for "space servers", around stealth for sure; to "scale it like a terrestrial DC" though ... dunno; not matter how I turn it, it just seems crazy expensive)
Communication latency and bandwidth would present big issues for AI satellites used for training. But if they are inference-only, then the latency and bandwidth demands are much, much lower. Starlink already demonstrates the required parameters.