Geostationary orbit is far higher than low earth orbit and I would assume following earths twilight zone would not be much better. I do not see why you would either, with reaction wheels you could orient the satellites towards the sun regardless of the relative position of the earth, with the caveat that earth may block the sun which is hard to avoid entirely anyways.

Also, there is not that much cool breeze in space, famously known for not having vast amounts of air (still have IR-radiation to help though).

Edit: Probably ate the onion, didn't I?

Again, I'm pretty sure they're aware that you need bigger radiators when you're using more energy. This is space engineering 101.