BATTERY FOR A MOTOR VEHICLE, AND MOTOR VEHICLE

A battery for a motor vehicle, with at least one battery module, which has a plurality of battery cells. The at least one battery module is arranged in a battery housing of the battery. The battery has a cooling device for cooling the battery cells by means of a cooling medium. The cooling device comprises at least one wall of the battery housing, with which the at least one battery module closely fits, and which is formed from a heat-conducting plastic at least in areas. The heat-conducting plastic restricts at least one duct for the cooling medium, with the duct being formed in at least one wall of the battery housing.