I update this just to re-confirm that the freezing problem has nothing to do with the console, the way it's set up, the disc, heating or anything like that. In case it wasn't clear enough yet.
My girlfriend started a Skyrim game after I finished mine, she's been playing for some time now, and her game works perfectly fine. No crashes at all, she can travel Skyrim from one end to the other without trouble. We're obviously using the same console, the same disc, etc.
So there you go. These are game issues. It's entirely Bethesda's problem. And I wouldn't be surprised if, once she is more advanced in the game, the crashes come back. I mean, I'm sure they will be back, this happens to pretty much everyone. What I'm curious about is when exactly.