A battery device has a battery housing, a plurality of battery cells arranged therein, around which a dielectric thermal management medium can flow in the battery housing at least in some areas in an immersion circuit inside the battery for the purpose of immersion thermal management, and thermally conductive elements. The thermally conductive elements are each arranged between two adjacent battery cells which each bear with at least one side against the respective thermally conductive element in thermally conductive contact with the latter. The thermally conductive elements here project in at least one direction beyond the battery cells and through a housing wall of the battery housing to the outside. The thermal management medium can likewise flow around those sections of the thermally conductive elements running from the battery cells to the corresponding housing wall.