System powers off during certain games

A couple of weeks ago I was ready for a new game and installed
Grand Theft Auto IV on the Windows XP side of my dual boot PC.
As I tried to play the game a very troubling symptom began to
occur... the display would freeze up and a few seconds later the
whole system would power off.

I tried checking the CPU temperature in the BIOS afterwards
but it was fine. However, this was after the system crashed and
rebooted so presumably it had some time to cool off.

I tried some other games and they worked fine, however, one
other game, STALKERS: Shadow of Chernobyl, was
getting the same failure mode, maybe a little less often.

Nothing in Linux was having any trouble including hi-res 3D games
like Urban Terror and DOOM 3.

I tried vacuuming out the case and all the fans, including the
fan on the graphics card. There really wasn't that much dust
accumulated and afterwards the system still crashed.

My gut is telling me the CPU is overheating so I ordered
one of these to try replacing the plain-vanilla CPU fan that
came with the CPU.

A colleague suggests my power supply might be too weak for all
the devices I'm trying to run off of it... something else to check.

The souped-up CPU fan arrived and I went to install it. There
was an unfortunate turn of events. I applied the thermal grease
to the fan as instructed and lowered it into place on top of the
CPU. I was in a hurry and careless and manhandled it into place.
Power on... nothing. I removed the fan again and found the
CPU stuck to the bottom of the fan, all cockeyed and with
numerous bent pins. What must have happened is the CPU
stuck to the thermal grease on the fan, got lifted out of its socket,
then was damaged as I tried to position the fan and lock it down.

I made a hasty visit to the computer hobby store. All they had
on hand in AM3 was an AMD 840. This is the low end of the
Phenom II 4X product line. It's a quad core but 3.2 GHz
instead of the 3.4 GHz of the AMD 965 I was replacing,
and it lacks a L3 cache.

The second, more cautious attempt at installing the fan was
successful. The temperature in the BIOS display is around 30 C
where before it was 60-70 C. But it's not really a good comparison
as it's a different CPU.

The problem I set out to solve appears to be fixed. I played both
games for a while with no crashes. I kind of think the cooling
theory was right, but something else about the old CPU could
have been causing the problem.

Update: A month or so went by and I was really noticing a
difference with the sluggish 840 CPU so I went out to Micro Center
and got an AMD Phenom II 975. It's basically the same as the
old 965 but 3.6 GHz instead of the 965's 3.4 GHz. I got this
installed without incident. GTA IV still runs without crashing
the system. This is more evidence that CPU overheating was
the problem. If anything this faster CPU should run hotter.

Amusing little irony... The AMD processor in a box comes with
the CPU, fan, thermal grease, instructions and a sticker.
The instructions advise that you will void your warranty if
you use your CPU with a fan other than the one provided,
yet it seems the stock fan is not really adequate for some
applications.