Does the computer Shutdown or Restart? its important as the problem can be 2 different things.
A Complete Shutdown is generally only caused by overheating
A Restart can be many things, from heat to RAM, motherboard, hdd, corrupt windows, video card and the list goes on.
Heat sounds like the issue, i would get a can of compressed air (hardware store) and give the CPU fan a good clean out.
see how this goes, if you still have issues you may need to take the fan and heatsinc off and re-apply some new heat transfer compound.
It was a heat issue. I had looked in the BIOS and the CPU was running at about 63C at idle, so it would be a reasonable conclusion that when in game, the processor would heat up to the shut-down I had set. The fan had already been blown out, so I got a better fan and heatsink (had been using the stock one), and that has so far done the trick
Thanks so much - I was kinda thinking it was a heat issue, but I was doubting my ability. Thanks again & have a great week!