CPU Temperature At Around 70C - Slowly Increases / Hits 100C And Shuts Down

My old computer's temperature sensor is either broken or I am doing something wrong. The general specs of it are:

Windows 7 Ultimate Edition
Intel 946G Motherboard
Pentium D 820 2.8Ghz
3 GB DDR2 533 Ram
ATI Radeon x1650 pro

When I go into bios and read the cpu temperature from there, it starts at around 70C and slowly rises until it eventually hits 100C and shuts down. This takes about 5-10 min before it hits 100C. When I enter Windows, it starts at around 60C and it actually goes up to 80C when I am playing games. This is way hotter than normal. It does not rise like in bios and goes back to 60C when idle. Prior to this, the temperature actually hit 100C and it shut down my computer. I bought a new heatsink thinking it would solve the problem, but clearly it did not. The temperature is still too hot.

Since a brand new heatsink did not work, I thought it was cpu problem for sure. I borrowed one of my friend's Celeron D and installed it. I entered bios and what do you know, it stays at 42C and does not even budge. So at this point, I'm 100% sure it's a cpu problem. I decided to buy an intel pentium D 945 3.4Ghz. I installed it and was extremely happy thinking my cpu's temperature would be decent. I entered bios and what do you know, it does exactly the same thing my 820 2.8Ghz did. It starts around 70C and the damn thing keeps on rising. So I decided to go into windows to see how the temperatures were in there. It idles at around 47-49C. When I ran prime95 for a test, the cpu went all the way up to 93C before I decided to shut it off and not do any further damage.