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.
This means you need some sort of heat pump. For a practical example you can look at the ISS, which has what they call the "External Active Thermal Control System" (EATCS), it's a complicated system and it provides 70kW of heat rejection. A datacenter in space would need to massively scale up such a system in order to cool itself.
Computers aren't humans. High-performance silicon can comfortably operate at a junction temperature of 80C to 90C (approx. 360K). Because of that T^4 relationship, a radiator at 85C rejects nearly double the heat per square meter than a radiator at 20C, unless I miss something.
So this makes it a bit more nuanced.