A wax-type thermostat for the cooling system of an internal combustion engine (ICE) provided with a radiator and a coolant loop circuit linking the radiator to the ICE, and a by-pass conduit. The thermostat comprises a thermostat body with one inlet from the radiator, one inlet from the ICE, and one outlet to the ICE. The thermostat further comprises a closure element integral to a first piston that closes or opens a thermostat internal pathway running from the inlet from the radiator to the outlet to the ICE, a main wax chamber thermally connected to the coolant within the thermostat body, and a spring to return the closure element towards its closing position. Also provided is a first means for moving the first piston when a volume variation in the wax occurs.