Motorcycle with a cooling system structure and a water-cooled internal combustion engine

In a cooling system structure for a vehicular water-cooled internal combustion engine (E) with a cylinder section and a cylinder body (41) and a cylinder head (42). The cooling system structure having water jackets (50A) formed in the cylinder body (41) and the cylinder head (42), respectively, with a radiator (52) disposed forwardly of the engine main unit. A water pump performs forced circulation of coolant through the radiator (52) and the water jackets (50A), to permit routing of pipes with enhanced appearance. Water jackets (50A) are formed, respectively, in a cylinder body (41) and a cylinder head (42) such that coolant flows through the cylinder body (42) and the cylinder head (42) independently of each other. A thermostat is mounted on a front wall surface of a cylinder section and is capable of selecting a condition in which the water jackets (50A) directly communicate with each other or a condition in which the water jackets (50A) communicate with each other via a radiator (52).