A melting and/or refining unit for conductively heatable melts, in particular glass melts, is provided. The melting and/or refining unit has a tank and at least one electrode. The electrode passes through an opening in a wall of the tank so as to be immersed in the conductively heatable melt. The melting and/or refining unit has an apparatus for reducing the local introduction of heating power into at least one region adjacent to the electrode.