A cooling device for a battery assembly, in particular a high-voltage storage unit, of an electrically driven vehicle has multiple cooling lines in which a coolant is conducted. The cooling device is designed to transfer heat from the battery assembly to the coolant. The cooling device has at least two individual cooling elements which are designed separately, which lie opposite a battery, and each of which is supplied with coolant via a dedicated valve paired with the respective individual cooling element. A unit including a battery assembly and such a cooling device are also provided.