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.
"More efficient cooling architecture taking advantage of higher ΔT in space"
My bold claim: The cost of cooling will not be $0. The cost of launching that cooling into space will also not be $0. The cost of maintaining that mechanically complex cooling in space will not be $0.
They then throw in enough unrealistic calculations later in the "paper" to show that they thought about the actual cost at least a little bit. Apparently just enough to conclude that it's so massive there's no way they're going to list it in the table. Table 1 is pure fantasy.