The invention describes a process for the electrolysis of an aqueous solution of alkali metal chloride, in particular sodium chloride, by the membrane process with an aqueous solution of alkali metal hydroxide, in particular sodium hydroxide, as catholyte, where the temperature of the alkali metal chloride solution in the anode half-element and/or the volume flow rate of the alkali metal chloride solution in the anode half-element are set in such a way that the difference between the temperature of the alkali metal hydroxide solution at the entry into the cathode half-element and the temperature of the alkali metal hydroxide solution at the exit from the cathode half-element are not greater than 15° C.