A battery system with at least one cell having an adjacent temperature-equalizing structure that is provided alternately with the cells and is designed for a medium that carries heat and/or cold to pass through. The cells are individual cells (1, 1′, 1″), and the temperature-equalizing structures are conventional corrugated board (2a, 2b, 2c, 2d, 2e, 2′a, 2′b, 2′c, 2′d, 2′e) having two cover layers and at least one corrugation arranged between them for the air to pass through.