A process and apparatus for removing molten glass from flow channels for the transport of production glass that are installed between a melting furnace and an extraction point for the production glass. The flow channel has a glass-resistant inner lining. A drainage unit for bottom glass is installed upstream of the extraction point for the production glass. In order to keep electrodes away from the molten glass, but still maintain a local and temporal influence on the temperature profile within the cross section, the inner lining, at least in the area of the drainage unit, is formed of a fusion cast electrically conductive material which has a drainage opening for the bottom glass with a drainage slit above it. At least two electrodes are installed on opposite sides of the flow channel and the drainage unit for the bottom glass. The electrodes are rod-shaped and their front ends are inserted so deeply into the inner lining in the direction of the molten glass, without contact with the molten glass, so that the majority of the electric current from the electrodes passes through the molten glass to reach an electrode plate installed below the drainage opening.