A method for operating a water electrolysis device produces hydrogen and oxygen from water. In the electrolysis device, water which comes from a PEM electrolyzer (1) is fed to a first heat exchanger (10) for cooling, subsequently to an ion exchanger (11), then to a second heat exchanger (12) for heating and again to the PEM electrolyzer (1), in a water circuit (4). The heat exchangers (10, 12) form part of a common heat transfer medium circuit (20) at a secondary side. The heat transfer medium circuit includes a cooling device (24), through which the heat transfer medium flow is selectively led in a complete or partial manner or not at all, for the control and/or regulation of the temperature of the water which is fed to the ion exchanger (11) and/or to the PEM electrolyzer (1).