We don't know who struck first, us or them, but we know that it was us that scorched the sky

That sounds familiar, like a quote from some movie or game. What's it from?

Overheat as there is no way to disperse heat in a vacuum

This is incorrect. You cannot do convection heat removal in a vacuum because there's no air. However, you can still do radiant heat dispersal.

So you dump your heat into something that has a lot of surface area with which to radiate it away from your components.

Space is either very hot or very cold, depending on whether you are in light or shadow. If one side is constantly exposed to light, then there must be radiators on the other side to radiate that heat back off into the cold.

I actually work in the space industry designing/building/testing satellites.

The answer is big fuggin radiators and perpetual night time sun synchronous orbit while the other vaporware/grifters trying to shill orbital power beaming blast your solar arrays with the power of a thousand suns every now and then.

There is math for it, and I have a fuck load of doubts, but people are funding this bullshit.