The invention relates to a battery cooling element having: an outer surface for resting at least in regions against a battery cell and/or for resting at least in regions against a battery module comprising at least two battery cells; an inner chamber for receiving a cooling medium, which inner chamber is surrounded at least in regions by the outer surface; and a cooling medium inlet connected to the inner chamber and a cooling medium outlet connected to the inner chamber, wherein the outer surface is made, at least in regions, of a thermally conductive, flexible film which can be shaped by a fluid pressure of the cooling medium.