Hmm. I haven't ever heard of a CPU overheating because it is faulty, but I am by no means the most experienced guy on here. There are a few things find out first.
1. What make/model is your CPU?
2. Is it overclocked at all? - If it is, try running at stock clocks/voltage.
3. Do you have the stock cooler that came with the CPU?
My first reaction would be to remove the heatsink block from the CPU, clean off the thermal paste, re-apply new paste and then refit the heatsink block making sure it's as tight to the CPU as safely possible. If it is still overheating, try a different cooler. If it's still overheating after that then it may be the CPU after all.
Hope this helps.