SamuraiHQ:
It could very well be an overheating problem, if one of your fans have failed (it happens). The next time it's off - take the side panel from the computer case off, and start it up. Without sticking your fingers inside, have a check to see if all the fans are spinning and working as they should. Might also be worth investing in an air duster to clean any dust and debris from the fans, memory sticks etc... so it's not hotter than what it should be.
When you start the PC up, if you can get into your BIOS (normally by pressing F8 a few times - depending on motherboard - instructions to do this should be advertised on bottup), you should be able to read the temperatures in some of the settings by manually going through the options at the top using the arrow keys and enter. You don't need to change anything, and you can always exit without saving any changes.
That would be my first guess, but it could be many other things which we can go into later.
Edit** This was meant to be the 2nd reply, but I spent too long typing lol. It seems someone else had the same idea ;)
(Hubby at home now)
i haven't checked the fans yet as the PC will freeze on start up when cold even when you have selected the user name.
About 5 weeks ago i replaced the graphics card as the original failed (the fan seized). The new card is a Sapphire ATI Radeon HD 4600 Series 1GB AGP card. Once installed everything worked fine until last week. I do play a game called Command and Conquer now and again and the freezing does seem to happen AFTER playing this game, but haven't played now for several days, but PC is still freezing (sometimes restarts without warning). One thought i have had is that i downloaded the latest graphics card driver and i think (not sure) that this problem has only started since download.