Are conventional fridge thermostats active or passive?
These things are strictly mechanical with the expansion of a gas in the capillary operating a snap-action switch. There is no electronics within and no potentiometer. 

You can test the switch operation by cranking the knob until it clicks on and off (and measuring the contacts) but to test the actual functionality you need to change the temperature of capillary. It's possible the capillary has been damaged and the gas has leaked out, but that's unusual without some visible damage.