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