Yes. It is very cold up there but there is also no matter, or very little matter. So head conduction and convection don't work, it's all radiation. When we are learning to solve heat transfer problems in engineering school we are generally taught to neglect radiation, because it's effect on cooling the system is typically second or third order when compared to the to "big C's"

It would take roughly 5000 square meter area to cool a typical small data center heat output (1 MW). Not great, not terrible.