Radiative heat dissipation is a function of the temperature difference between the fourth powers of both source and sink, multiplied by the area of the radiator, its emissivity, and Boltzmann's constant.
As I'm sure we all know, a computer basically turns electrical energy into heat. If this satellite is generating 1KW, it needs to radiate the equivalent quantity of heat to remain at whatever its operating temperature is - for the following calculation I'm going to assume this is ~80 C (~353 K). And, to make life easy, I'm going to round down the temperature of empty space to 0 K. Finally, let's assume a perfect emissivity of 1. This essentially gives us the 'best case' scenario, i.e. the minimum radiator size we can get away with...
Required radiator area = 1,000 / (5.67e-8 x 353^4) = ~1.14 m^2
You all might want to check my maths here!
Because, honestly, this is a lot lower than the figure my intuition was telling me. Additionally, it occurs to me that putting a closed loop heat pump between source and radiator would further decrease this required area (by boosting the temperature of the radiator further), whilst at the same time boosting chip cooling, albeit at the cost of additional power. Ok, sure I made some simplifying assumptions, but even a 20% increase in required radiator area doesn't put us into the realms of engineering impossibilities.
On balance, the thing that really blows my mind about this news is the power requirement of the TPU's in the first place. >1 KW? For a single chip? No wonder these companies are looking at putting them up into space. The payback time will likely be measured in months, not years...