*If the 360 isn't over heating.......
* If you cleared the cache, it also removes any update's that were downloaded. Which could be a problem, if so try downloading them again. Any saves that rely on deleted updates won't load correctly and can cause funny crashes or freezes.
*Turn off auto-saves ... for some reason they cause a lot of issues. ( just make sure that you manually save often). ...
* If you have a friend with a 360, see if your disc causes issues with their game ( always a chance, just make sure they have a couple hard saves)
* try un-installing and re-installing the game with your disc. make sure to revert to a save before you had issues, as those problems are already baked in or start a new game altogether. I made a habit of completely clearing out my 360 every couple of months.