@ChrisHolladay @Adventurer I'm coming to this thread really late. So late, I don't know what started this, so take this with a grain of salt.
The thermostat is probably supposed to be attached to metal for it to operate. In that case, if it is hanging loose, it's just measuring ambient air.
I can't tell if the rivet has anything to do with attaching the thermostat, but if you found it was loose to begin with, that might have been a problem.