Repairing a heat gun
How dangerous?  Very. You might not die immediately, but something bad will happen eventually.

Look at it this way, something made the thing overheat and the safety device kicked in.  Now, you want to remove the safety device not not fix the thing that made it activate in the first place.  So now you have something dangerous and no safety device.

Heat guns are cheap.  Throw that one away and buy a new one.  Is your life and/or home worth the $25 for a new one?