@ Darias and Ravenstrike: The Devs (and us testers) are aware that currently there are some pretty bad memory leaks in the game. This is the most common cause of current "unexplained" crashes I'd imagine. Of course there are other crash bugs, gameplay bugs, bugs related to systems not fully implemented, etc etc, but it shouldn't be locking up systems or causing systems to overheat and shut down. Things like the later definitely deserve a bug report to be filed.
On a side note, a few years ago on a older rig I had there was this problem. I was running a GeForce 7 series video card and I'm a cig smoker. I have a few air purifiers now to solve the problem but back then cig smoke build up would become a problem. Eventually the fans in the video card and my power supply gunked up. They would over-heat and shut down my system but Only when I played games that really stressed my system as these would be the games that would push the system to turn on those fans when temps hit a certain level.
If your comps are working with other games, but not Elemental, check a few other "New" games and see what affect they have on your systems. Games that you've ran for a while now may work fine, while newer games that push your system harder may cause it to over-heat. Just a thought and something to look out for. Also take note you don't need to be a smoker for this to be the case as normal dust accumulation can cause the same thing to happen it just takes a lot longer then it does for a computer in a smoking environment.
I also ended up buying some hepa-filter bags for computers that run in industrial zones. They do increase the internal temp by 1 degree celsius but they keep out All smoke while still allowing your computer to breath.