A water-cooled internal combustion engine, in particular for equipping scooters and motorcycles, having an engine block, obtained from one only single-piece melting and with a driving axle substantially perpendicular to a longitudinal development of the internal combustion engine, and a cooling system comprising a radiator, a relative fan and a water circulating pump comprising a intake nozzle and a discharge nozzle, wherein the fan of the radiator is fitted directly on a crankshaft, therefrom even the driving force for said cooling water circulation pump is derived, interposed between engine block and the radiator, the radiator being arranged laterally to the engine block, with the fan lying on a plane substantially parallel to said longitudinal development, wherein said circulating pump is arranged on the opposite side of the engine block with respect to the radiator, the cooling system comprising: • a first cooling circuit having: o a discharge line and a extraction line connecting the radiator to said engine block, said lines (16, 17) being constituted by tubes outside the engine block with respective discharge openings, formed in said engine block, and intake opening connected to said intake nozzle of the pump; o an inner circuit portion (24, 25) for extracting heat from the engine; • a second cooling circuit wholly included in said engine block for recirculating the cooling water, comprising a by-pass line, connecting said discharge opening to the intake nozzle of the pump, and said inner circuit portion (24, 25) for extracting the heat from the engine; and • a by-pass valve, arranged on the engine block at said discharge opening, actuated by a thermostat sensible to the water temperature, allowing the water circulation either in said first cooling circuit, above a reference temperature, or in said second cooling circuit, below said reference temperature, between the fan and the engine block an electric motor being arranged, operating as starter motor and as current generator, the rotor thereof being fitted onto the crankshaft. • a first cooling circuit having: o a discharge line and a extraction line connecting the radiator to said engine block, said lines (16, 17) being constituted by tubes outside the engine block with respective discharge openings, formed in said engine block, and intake opening connected to said intake nozzle of the pump; o an inner circuit portion (24, 25) for extracting heat from the engine; o a discharge line and a extraction line connecting the radiator to said engine block, said lines (16, 17) being constituted by tubes outside the engine block with respective discharge openings, formed in said engine block, and intake opening connected to said intake nozzle of the pump; o an inner circuit portion (24, 25) for extracting heat from the engine; • a second cooling circuit wholly included in said engine block for recirculating the cooling water, comprising a by-pass line, connecting said discharge opening to the intake nozzle of the pump, and said inner circuit portion (24, 25) for extracting the heat from the engine; and • a by-pass valve, arranged on the engine block at said discharge opening, actuated by a thermostat sensible to the water temperature, allowing the water circulation either in said first cooling circuit, above a reference temperature, or in said second cooling circuit, below said reference temperature,