A cooling system for an internal combustion engine of a motor-vehicle presenting a circuit (1) for a coolant of the engine. The circuit (1) comprises a thermally insulated tank (6) for the coolant of the engine, connected to an outer portion of the cooling circuit (101). The tank (6) is arranged in the circuit (1) to retain a defined quantity of coolant at a temperature above the ambient temperature when the engine (2) 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 (2), after a subsequent start of the engine (2), during an engine warm up stage. The circuit (1) also comprises an expansion vessel connected to the outer circuit portion (101) of the coolant of the engine (2). The expansion vessel has a thermally insulated body and constitutes the thermally insulated tank (6) for the engine coolant.