if you haven't already, clean the CPU cooling fins.
I'm not familiar with the OS that you are using so the help here is going to be general.
This is probably a OS issue common to the XP family. There are hidden updates/fixes that address this issue so unless you go looking for it it's unlikely to be found.
There's a setting somewhere in the XP OS that might allow you to prevent an instant shutdown at least long enough to give you a BSOD (and a memory dump written to HD), if it does, write down all the info that is provided before going further.
You might check to see if there are any drivers that need to be updated (Windows Update isn't going to notify you of all of them) specifically those that apply to your VGA adapter. Also check for BIOS upgrades.