An eddy-current brake device includes at least one heat exchanger for dissipating the thermal energy that is due to the eddy currents during braking. The heat exchanger is designed to define a path for the cooling liquid, which path is predetermined in order to minimize the pressure drops and maximize the rate of flow of cooling liquid circulating through the exchanger, with a view to reducing the variations in working temperature of the heat exchanger. The device may include two symmetric heat exchangers, of which the inlets, the circuits and the outlets for water are arranged symmetrically, so as to compensate for the forces due to the currents of cooling liquid and so as thus to minimize the corresponding residual torque.