Your problem can be either software or physical at this point (which you seem to know). None of the issues you mentioned are standard or widespread on the forum so I'd assume they're specifically issues on your end, and thus, something to do with your system in some way. I'd assume it's heat-related (as you surmised) because it does get steadily worse after a set amount of time. If you've given the system plenty of room to breathe and don't have it sitting on a carpet/floor and not on a soft surface, then it reduces that chance, but it really all depends on things. If other games lock up after a set amount of time as well, then this probably is your issue; if not, then it may be the Destiny files. If you have no other games to check or they don't lock up as well, then I'd recommend doing the uninstall/reinstall first, as that's something you can do without chancing blowing more dust around inside your system (which can cause its own problems). If an uninstall/reinstall doesn't fix the issue, then I'd work on cleaning the system, but take care when you do so; try not to jostle the system if you can help it, even though it's going to be unplugged (unplug it and take any disk out that's in it). Good luck!