Save. clean kitchen image by easaab from Fotolia.com. A refrigerator thermostat has only one function -- controlling the refrigerator's cooling system by turning it on or off to ensure that the temperature inside the fridge stays in the correct range of 33 to 40 degrees Fahrenheit.In frost-free models, a separate thermostat with a timer controls the defrosting cycle.ave. clean kitchen image by easaab from Fotolia.com. A refrigerator thermostat has only one function -- controlling the refrigerator's cooling system by turning it on or off to ensure that the temperature inside the fridge stays in the correct range of 33 to 40 degrees Fahrenheit.