I haven't had this problem in a while, but I thought it was extremely strange when I saw the temp for the first time.
Anyway, my old computer (which my brother is using right now) was an AMD K6-2 running at 350 Mhz. It was not overclocked(not by me, anyway). Generally, it ran at around 30 to 40 degrees CPU core temp. However, sometimes(about 10% of the time) I played a certain game (not demanding of it's spec, Duke Nukem 3d), and ALWAYS on a particular level, regardless of length of play, the Computer would emit(from the pc speaker) it's temperature siren (the first time, as one would expect, it scared the crap out of me) would blare. The first time it happened I quit and start MBM to view temps, and the CPU core was at over 80 degrees celsius. Case temp was 60 (ambient temp was I believe around 18). Crazy I know....
The problem being that although I would like to install a new cooling solution, I'm afraid the power supply wouldn't be able to handle it. The poor thing can deal with the system when I had it fully loaded (all slots where full, memory maxed out, not to mention 3HD drives and a Optical drive.(Drives would dissapear, HD would lose power, loads of fun) (I of course have reverted it to a more stable configuration).
I would appreciate any suggestions, I just think it's messed up, on account of even the newest processors idling at lower temperatures.