Sadly no I don't have another system to test my components on and a spare psu to work on. I've tested it out on while the case lid was open yet it still shut off while playing assasins creed on medium settings even though I have a pretty high end graphics card. However it doesn't shut down when playing other games like spore on high setting that run at least 20 FPS with other programs (Firefox, Skype, etc...) in the background. It also shuts down when trying to start up again after a random shutdown.
So you may be right about the heat issue
So in short:
It turns off only when playing Assasins creed and watching videos on hulu longer than 10 minutes
when turning it back on after a random shutdown there is a 70% chance that it could shut down again.