The system has a temperature-control system (20) comprising a liquid temperature absorption control medium for cooling and heating battery cells (13) in a battery housing (10). An absorption element (30) is arranged between the battery cells and the battery housing and absorbs the liquid temperature-control medium discharged from the temperature-control system. The absorption element is composed of non-woven material including supporting fibers or absorption fibers, where the non-woven material has average area-related mass in range between 250 to 700 gram per meter square.