A cooling system for an internal combustion engine of a motor-vehicle presenting a circuit for a coolant of the engine. The circuit includes a thermally insulated tank for the coolant of the engine, connected to an outer portion of the cooling circuit. The tank is arranged in the circuit to retain a defined quantity of coolant at a temperature above the ambient temperature when the engine is inactive, and for causing this quantity of coolant to flow, at a temperature above the ambient temperature, into the cooling circuit of the engine, after a subsequent start of the engine, during an engine warm up stage. The circuit also includes an expansion vessel connected to the outer circuit portion of the coolant of the engine. The expansion vessel has a thermally insulated body and constitutes the thermally insulated tank for the engine coolant.