But assuming your radiator is going to be hot anyway (we've got a Dyson sphere to produce all this problematic energy, right?) then surely it's not that big a deal?

Still, it gets me thinking science-fictionally. Are there any stories where aliens invade the Earth just to use it as a heatsink? Travelling around from star to star, dumping all your waste heat into whatever planets you can find -- sounds like a great lifestyle.