It still sounds to me like the processor overheating. Have you tried running Prime95? That will really tax your processor. Is your CPU overclocked at all, and what kind of CPU cooler do you have?
I am using the stock CPU cooler and I have not overclocked it at all.
I ran Prime95 using the test that is supposed to max the CPU and power consumption and it passed. Looking at Core Temp, the processor never went over 61 degrees Celsius and my computer didn't shut down.
I also ran a benchmark in 3DMark06. It ran fine, here are my results if you are interested: http://3dmark.com/3dm06/16709393
I know there are some system graphics demos out there, but I have never used them. With some tool like that, I wonder if you could create a heavy load for the CPU and GPU and then see if you experience a similar shutdown?
This comes to mind:http://developer.amd.com/samples/demos/pages/froblins.aspx
Like I say though, no idea if that would be any useful indicator.
I ran that demo as well. It was kinda entertaining watching thousands of frogs walking around in platform shoes carrying rocks and eating shrooms and then passing out.
My PC handled it fine.