This could be happening because of a few different reasons, let’s try to narrow it down and figure out why it’s happening.

When people say freezing it usually the other way around, (your Xbox is actually overheating.)
Depending on how many hours your Xbox 360 is on could be the main cause of your games freezing up, however that’s not always the case, it’s been suggested that there’s an actual failure with the GPU processor and why it freezes up.

The best way to get around your Xbox from freezing up is to install an extra cooling system, a cooling fan of some sort. It’s recommended, that you do install an extra cooling fan because the Xbox 360 is well known for overheating, plus when you install a new cooling fan or replace the original you’ll notice a big difference in sound, "allot quieter".

You can go to consoles shop and get yourself a whisper fan, there really affordable and easy to install and make a world of difference, I’m not guaranteeing you that it will fix the freezing problem but I can promise you, that you won’t have any more problems with overheating. Seeing how they’re both related it won’t hurt.

But if you’ve already been through that or tried some how to prevent your Xbox from overheating or maybe you have even gone as far as already installing a new cooling system, it’s most likely going to be a GPU processor problem, just like with anything else, things get old from wear and tear that’s normal.

You might not need the even to replace the GPU it could be just gunked up with gunk and all you need to do is clean it, you can watch a few videos found on this site, here’s a link to learn how to dismantle your Xbox 360.

Whatever the actual problem might be, you’ll find that it’s actually something very easy to fix, overheating and freezing are so common that it’s nothing to be too worried about.

If you’d like to learn some great prevention tips "Xbox 360 preventive maintenance" I highly recommend getting the Xbox 360 red light fix guide that will teach you and show you every trick and tip there is, to keeping your Xbox 360 in tiptop shape especially from freezing.