Dont reassemble the hsf of the P3's - youll prolly break it gettin into it (P2's were easy, the P3 S1's wernt).
Actually, there is a nifty little trick you can try when you've got the open-end Slot 1 cartridge with the snap-in HSF clips (a la OEM P3). You can use a typical case screw to push the snap-in posts back out--just set the screw head-down on your work surface, set the CPU on top of it so the snap-in post nestles in the end of the thread shank, and give it a moderate-force push. I've actually done that quite a few times, and the whole thing goes right back together without a problem.
Retail HSFs for that cartridge usually had the posts going all the way through and sticking out the backside of the cartridge, with some kind of removable latching mechanism gripping the ends on the backside.
As far as the temps go, I bet we're all wondering why exactly there are two temperature readings being reported for the CPU. I'd suspect one might not be the CPU at all, but might be a thermistor elsewhere on the motherboard, maybe placed to pick up ambient or chipset temperatures. Or it might be a GPU temp sensor? Who knows. 80C definitely sounds too high though, whatever it's measuring.
I'd see which sensor shoots up when you run Sandra's CPU burn-in test. That'll be your CPU temp.
P.S. I first played Unreal on a P2-300 with a 12MB Voodoo2. Man, it was sweet. 8)