I would not assume cooling has been worked out. Space is a vacuum. i.e. The lack-of-a-thing that makes a thermos great at keeping your drink hot. A satellite is, if nothing else, a fantastic thermos. A data center in space would necessarily rely completely on cooling by radiation, unlike a terrestrial data center that can make use of convection and conduction. You can't just pipe heat out into the atmosphere or build…
Thermos has 2 parts responsible for thermal isolation: vacuum and some coating that reflects heat radiation
Also in earth conditions, most of thermal radiation goes to surrounding air, heating it. This is not the case with vacuum, so thermal radiation will be even more efficient