A battery system includes a plurality of battery cells and a temperature-control element that is thermally conductively connected to the battery cells via a temperature-control surface. The temperature-control element has a temperature-control channel in an interior of the temperature-control element. The temperature-control channel is routed on the forward flow side via an inlet and on the return flow side via an outlet from the temperature-control element. A bypass is connected to the temperature-control channel via a dividing node and a merging node with the dividing node being arranged closer to the inlet than the merging node. A motor vehicle includes the battery system.