The invention relates to a water electrolyser (2), comprising: an electrochemical cell (21) for electrolysis of water comprising a membrane / electrode assembly (31) including a proton exchange membrane (311), a first face the membrane / electrode assembly having an anode (312) and a second face of the membrane / electrode assembly (31) having a cathode (313); -a power supply (7) configured to apply an electric power or a current or a potential difference between said anode and said cathode, said electric supply (7) being housed in a housing (70) in which an air cooling circuit (700) is provided between an inlet (701) and an outlet (702) of the housing, the power supply comprising a fan (703) configured to generate an air flow through said circuit (700), said outlet (702) ) emerging at an upper part of the electrolyser. Figure to be published with the abstract: Fig. 14
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