Abstract: A cooling box adapted to be installed in the refractory wall of a steel-making arc furnace for passing a cooling medium therethrough to cool the wall. The box comprises a base plate having an inlet and an outlet for the medium, a heat receiving copper plate having a slag lodging portion over the heat receiving surface thereof and a curved portion at each of its upper and lower ends for preventing cracking against thermal and mechanical stress concentration, and a back plate disposed between the plates closer to the heat receiving plate. The back plate and the heat receiving plate define a cooling medium flow chamber in communication with the inlet and the outlet and divided by a plurality of partitions to provide a flow channel of reduced cross section over the entire area of the heat receiving plate.