An aqueous electrolyte aluminum-air battery comprises one or more cells (14), each cell comprising a frame (40) which defines an electrolyte chamber (54). The frame (40) is made of a rigid material inactive to the electrolyte. The cell has a consumable aluminum anode (80) and an air cathode (90) spaced from the anode by said electrolyte chamber. Means are provided for admitting electrolyte solution into the electrolyte chamber (54). A vent (64) exposes the electrolyte chamber to atmosphere. A hydrophobic membrane (66) which is impermeable to the passage of electrolyte but permeable to the passage of hydrogen closes the vent. A surface (82) of each cell anode is exposed to the flow of air. The amount of surface exposed is effective to dissipate heat generated at the anode (80).