Shut Down

Hey guys have a problem with my 'puter.

Today it started to shutdown by itself. The first few times it actually did a shutdown fully, but now it just simply shuts off.

This sounds like a heat problem, but what I am curious about is in everyones opinion whats the most likely piece of hardware?
I am currently thinking Power Supply since it simply shuts down without doing a "Shutdown" now. Kinda like a progressive PSU dieing type thing.

Whatch all think?

We need a little more info here, Is this a laptop or a desktop? What OS are you running? This can be a number of things, from A Virus to a bad cpu fan..

Desktop.
AMD Phenom II x4 955cpu
32-bit Vista Home Premium
4gig Ram

I run Avast Virus. It has just started doing this particular thing. I can run World of Warcraft in Windowed mode but not fullscreen.
It has also shut down when I was playing a Java based game the other day with my kids, I did happen to have alot of windows open.
I have popped the case and see that all the fans are actually spinning, including the PSU fan.
I got a program called SpeedFan 4.49 to see if the Temp or Fan speed was off. Its a little confussing but it looks like it monitors the CPU, GPU and Case fan.
It seems that the CPU is running @ 3000-3900 rpm, the chasis is running around 2000rpm and the GPU is running 1600rpm at "rest" to around 1750rpm running WoW windowed on 2/3 rds of the screen.
Is there perhaps a program that will log system rescources on the fly so I can make it shutdown and have the info on what caused it?

EDIT: I ran WoW in windowed mode for a long time and nothing, but I enter a dungeon (ussually more intense graphically and CPU wise.) and was able to make it turn off after 3 or 4 mins.
I will try dumping all my graphics settings right down and see if puting less load on the system makes a difference.

So is this happening all the time or only when you are playing a game ?Sounds like it is getting too hot then shuts down...Will this happen if just running the computer normally ?

well.
the first time it actually "shut down" as in closed all the programs and shutdown like windows does, I was playing a online browser game.
It did that a couple of times when trying to start WoW. Now it just shuts down as in oops now you have a blackscreen and no Power running through the system.

Incidentally I have a GeForce 8800 gts gpu, which I pulled out after this started to happen and took the shroud off and blew it out etc, but it still crashes out under load it seems.
And after this started my wife and I played music on it for 3 or 4 hours, so it really seems like it only happens when there is graphics load on.

i would change the video card to another one, and also try another Power Supply.. check your fans, mainly the one over the cpu..

Most probably the problem it's your video card.Check the temps of CPU and GPU under heavy load.