A thermistor is simply a resistor that changes the resistance based on the temperature.
Many fluke and other VOM's include a thermistor mode where it turns the VOM into a temp sensor by converting the resistance into degrees temperature.
It often looks like a wire, or actually two wires, since you need a completed circuit. On an engine, a thermistor can have one wire since the block is the ground and the other half of the circuit.
In the fridge, it will probably have a jacketed wire with two conductors that will go back to the temp controller.
If the fridge "black wire" is very stiff and does not appear to be insulated, it is probably an old style capillary sensor that goes back to a thermostat. Those cannot be kinked or it will seal off the capillary and stop the pressure from getting from the sensing tip back to the thermostat. Here is an example of the fridge one...