You have a brilliant idea. It's famously efficient and possible to cool things by just separating the hot parts from the cool parts using a little divider called a Maxwell's Demon. You and the Moon summon one real quick, the Moon being real expert on occult knowledge, and you quickly set the demon to work. The demon's task is simple: determine what is hottest on your satellite, then eject the hot thing into space. It's just you and the Moon here really, and after some deliberation the demon decides you're hotter. Well, it's a fair cop, you are attractive. So to cool the satellite they jettison you into space and the Moon and demon keep going while you float peacefully off into the far reaches of the cosmos, still aglow with the compliment on your appearance.