When heated they expand at different rates and the thermostat bends, breaking (or making) a circuit.

They are very slow acting but do have an accuracy of about 1%.

When used in furnace control systems they switch off the power when the furnace has reached the correct temperature.

As the furnace cools the thermostat cools, and when the temperature has fallen by about 15 degrees the thermostat reapplies the power.