No, it should not be doing that, now who ever built your pc must have forgot the thermal paste.
Just to verify get a camera open up your case take the heatsink off gently and take a picture and post it back here promptly.
The reason why I ask this, 2 things I am checking for is thermal paste on cpu and if there are any burn marks.
If you have burn marks on your cpu, that could be a bad sign that your killing it by turning it on without any grease.
When I first built my computer back in 2001, I killed it by accident, reason being: thermal grease or paste, it was a nice 1.8ghz celeron...