These aren't big things, they're small satellites. They're going to be ~100kW. They only need to 5x the existing radiator they think will work.

Geostationary satellites are not standing still. They're orbiting the Earth at the same rate that it rotates "beneath" them.

Um, it doesn't make the data center in orbit thing make sense, but a geostationary satellite absolute moves at high speed and does not stay in the same place in space.

Super heat what in that space? The point is there's nothing to transfer heat to. All you can do is radiate infra-red light.

Radiators in space work by radiating electromagnetic energy(light). Heat can only accumulate in matter, not in space, so that is definitely not one of the things we need to worry about.

geostationary then its even harder as the the data center doesn’t move away from the heat.

Geostationary would leave the satellite in shadow anytime it was night time over the part of the earth since a geostationary orbit is stationary in the sky over a given point at the equator.

That doesn't solve any of the cooling problems just saying that you do get some shadow at geostationary orbits.

There are other orbits that get less shadow though.

Obnoxious as he seems to be, he's actually right, there will be no convection, but they'd radiate heat in a vacuum, by IR IIRC.