BSOD during Skyrim, possibly overheating?

Hello,
Just lately my computer has been struggling to play Skyrim, Assassin's Creed: Revelations and other recent(ish) releases. It usually crashes 20-30 minutes in, however reducing the resolution of the game (down from 1920x1080) or playing in a window seems to extend the time I can get before a crash. Additionally, not all the time does my computer even get to the blue screen, it often freezes, becoming totally unresponsive to any commands, whilst playing a loud buzzing sound, requiring a manual restart. As the title suggests, I'm not sure if it's simply overheating, or if it's something more.
Currently, my specifications are:
Windows 7 Ultimatex64
6 GB RAM
AMD Phenonm II x4 965 3.40 GHz
Nvidia GeForce GTX 560 Ti

Thanks,
Michael

I did both of those steps and so far it's been working without a single issue (many more hours of gameplay than usual and not as much heat), thanks so much; the perfect christmas present .

I've smashed out a fair amount of hours since, without any problems, although my brother said it crashed today when he was playing skyrim (i was out all day) however I'm not sure if it's the same issue or not; I can't find any new bluescreen dumps. He's quite a bit younger and only fairly new to computers and whatnot so i couldn't really suss out what went wrong, could be nothing.

Over the last couple of days I've tried a couple of other games:
I had a crash and forced reboot during Dawn of War 2, as well as Borderlands (whilst lan-ing with a friend), so i'm guessing that Skyrim isn't the culprit? (the sole one at least anyway).

Firstly, sorry for the break, i've been away for the past week, when i went to look there were no new dumps, still only the original four. i'll post back here as soon as i have something to report though. (thanks again for still being so helpful)