A synchronous generator, in particular a multipole synchronous annular generator of a direct-drive wind turbine, for generating electricity, with a rotor and a stator, wherein the stator has multiple grooves in which a stator winding is arranged, wherein the stator winding releases heat energy as a result of the generation of power, and wherein a cooling body for absorbing and dissipating released heat energy is arranged in one groove, multiple grooves or all of the grooves.