ONe thing you need to look at is AIR Temperature when looking at this problem..

Expect the temperature to rise on the CPU when its usage reaches 100%.. and depending on the cooling /airflow in the case this can be slow or very rapid.. the better the airflow the slower the temperature rise as also the lower the room temperature ..
Certainly with the Intel chips don't let them go into the 60's from memory 65deg C is the start of the death zone..

Edit\ check that the BIOS alarms havent been fiddled with.. these are normaly set in the late 40's iI normaly set to 53-55 for my machines..(these run 24/7 at or near 100% CPU usage and the room temps WILL reach 40deg C)