CPU Cooler Fans are not the same as a GPU Fan which can stop if cooler than a certain temperature.
If the CPU Cooler fan were to stop it will cause any processor to overheat within seconds and shut down the computer. They are built to run constantly.
You can control the SPEED of the fan, either via BIOS or Software, to make it less noisy when not under heavy loads but none will cause the fan to stop.
