I have a 3 year old Dometic fridge without 12 volt operation, hence no thermostat. I've tried moving the thermistor around to adjust the temp with little success.
I ordered an Inkbird 12 volt thermostat.
I use it to control the main power to the fridge, cutting power when it reaches 32. I set the temp differential at 2 degrees so it comes on at 34.
Wiring comes in through the drain hose.
It has worked well with ambient temps ranging from 38 to 99. Power consumption is .7 watts when engaged for cooling. Less when not cooling plus the fridge circuit board is not drawing any current.
Precise temp control for $15. Works for me.