Norcold gas & electric fridge

I'll put in my 2 cents worth. The problem with the propane end I would think would be the sensor on the tip of the ignitor, the flame not running perfectly, slow propane through the tube but that would set the sensors off and completely shut down. Lots of trouble shooting for the road. You mentioned you turned on the electric. Did you mean 12 volt or 110? 110 it should have cooled rite off but 12 volt would take a long time to cool off as is stated on the thread. Is the door closing completely? Is the light turning off when closed. Is the rubber gasket around the fridge door intact, clean and installed properly? These are the simple things I thought I'd add because all the mechanical things are already being covered.

https://www.rvrepairclub.com/video/troubleshooting-rv-propane-refrigerator-014996/

Your model number would help.