Abstract: A hydraulic shock absorber for a motorcycle employs a jacket which surrounds the damping chamber of the shock absorber. The damping chamber contains damping fluid and a damping piston for providing reciprocating axial damping displacement in accordance with axial forces exerted on a shaft connecting the damping piston. The jacket forms an annular outer chamber. Fluid circulates through the outer chamber to stabilize the temperature of the damping fluid in the damping chamber. The outer chamber is connected for fluid communication with the cooling system of the vehicle engine.