When I was having stability problems on my last rig, I used Q3 to test it too.
Set up a single player skirmish with bots, timelimit 0, fraglimit 0. Start the game and then go to the console and type /team s. This will remove you from the game, and the bots will fight indefinately. Personally I liked to use Q3DM17 filled with bots. There were so many bots to draw at one time that it really stressed the system.
/cg_drawtimer 1 can sometimes help determine when it locks up. If it bluescreens while you're asleep though, it doesn't help much. =)