> I think you're more likely to freeze to death, because temperature in space is near zero Kelvin.

We're talking about a civilization on board an interstellar ship that had to leave their home planet because they were consuming so much energy that the resulting waste heat ended up making the oceans boil. So the assumption that they'll keep on consuming lots of energy (and producing lots of waste heat) on board such a ship sounds rather reasonable to me.

> Inside the solar system however, you could reflect away the received radiation (and heat) using mirrors.

The discussion is about getting rid of heat produced on board the space ship, not heat that's received from elsewhere.