The valve core contains a specially designed wax. The wax expands as it is heated, forcing the valve open and allowing engine coolant to flow to the radiator. When the wax cools and contracts the valve is closed by a return spring.
More modern cars have a "map controlled" thermostat. These incorporate a heating element to melt the wax prematurely if the engine computer demands more cooling.
Here is the full video with narration.
And credit to Jalopnik for the animated gif.
