Right up to the radiation limit and then you'll either have to throttle your precious GPUs or you'll be melting your satellite or at least the guts of it. You're looking at an absolutely massive radiator here, many times larger than the solar panels that collect the energy to begin with.
> > absolutely massive radiator here, many times larger than the solar panels
> A_radiator / A_PV = ~3;
Seems like you're in agreement. There's a couple more issues here--
1. Solar panels are typically big compared to the rest of the satellite bus. How much radiator area do you need per 700W GPU at some reasonable solar panel efficiency?
2. Getting the satellite overall to an average 27C temperature doesn't necessarily keep the GPU cool; the satellite is not isothermal.
My back of the envelope estimate says you need about 2.5 square meters of radiator (perhaps more) to cool a 700W GPU and the solar panel powering the GPU. You can fit about 100 of these GPUs in a typical liquid-cooled rack, so you need about 250 square meters of radiator to match one rack. And, unfortunately, you can't easily use an inflatable structure, etc, because you need to conduct or convect heat into that radiator.
This assumes that you lose no additional heat in moving heat or in power conversion.
And they’re going to mass a -lot-. Not that anyone would use a pyramid— you would want panels with the side facing the sun radiating too. There are plenty of surfaces that radiate more than they absorb at reasonable temperatures in sunlight.
Datacenter capacity (and thus heat) grows by the cube law, but the ability to radiate heat grows by the square law, so it seems like it would be advantageous to have a bunch of smaller satellites, if you were concerned about cooling them.