Personally, my computer has failed so many times that I considered trashing it. When I sent it in for repairs, it turned out that both the fan and cooling unit were malfunctioning! Heat can do strange things to hardware; even if the hardware is rated for said heat, constant head over an extended period will cause strange problems which are hard to diagnose.
That said, it's possible your computer may in fact be crashing - it's just completely losing power instead of showing a blue screen. However, this may or may not be the case.
I suggest you use the Vista event viewer, here's how to access it: Open the start menu, and type "eve" in the search box. Select Event Manager, and check through each of the logs to find an error that corresponds with your crashes; they are labeled by time and date.
If you cannot find an error that corresponds with the power-down, then the possible options are: the PSU, the video card, and the motherboard. Further instructions can be provided based on your response to this.
But seriously, getting the temperature of your computer down is definitely necessary, no matter what the problem ends up being.
