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…
Can’t you heat exchange inside the satellite, and make one part of the satellite incredibly hot so that it radiates a lot and dissipates. This is just a question. I have no expertise at all with this.
On the similar lines, why can't one run a refrigerator in space?