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 a heat exchanger. You can't exchange heat with vacuum. You can only radiate heat into it.
Heat is going to limit the compute that can be done in a satellite data centre and radiative cooling solutions are going to massively increase weight. It makes far more sense to build data centers in the arctic.
Musk is up to something here. This could be another hyperloop (i.e. A distracting promise meant to sabotage competition). It could be a legal dodge. It could be a power grab. What it will not be is a useful source of computing power. Anyone who takes this venture seriously is probably going to be burned.
A satellite is quite unlike a thermos in the sense that it is carefully tuned to keep its temperature within a relatively narrow band around room temperature.[1] during all operational phases.
This is because, despite intended space usage, devices and parts are usually tested and qualified for temperature limits around room temperature.
[1] "Room temperature" is actually a technical term meaning 20°C (exceptions in some fields and industries confirm the rule).
Yes 20 and 25°C I believe are the two most popular choices. In many cases it makes little difference with units in Kelvin ¯\_(ツ)_/¯