There is not a compressor but the flue on the right (vertical galvanized pipe) can be 180 degrees. The tube that comes out of the bottom of it and then goes into a round cylinder can be just as hot, but the cylinder and the coils above it are closer to 130 or less so this area is normally hot.
Unhooking the thermistor makes it go into continues cooling but if you do not hear the fans running at the back, it's not going to cool properly when it's 80 out. You should be able to hear the fans if you listen at the door you took off. Are they running? If not put a fan in the opening to get enough air flow for it to cool properly.
My guess is that you caught it when it went into a defrost cycle which can take several hours. This happens every few days and when it's hot out it's enough to make it look like you have a problem. By shutting it off briefly every two days you can stop it from going into the defrost cycle which will help when it's hot out. I would hook the thermistor back up so you can start monitoring the fin temperature. By pressing both the Mode and Temp buttons down at the same time for several seconds you should see 88. Then press the mode button three times you will see the fin temp reported by the thermistor. The fins need to be in the low 20's for it to get the lower door temps below 40. Hope this helps.