A battery includes at least one integrated first heat exchanger element that forms an integral part of the battery and is formed in one piece with the battery. The heat exchanger element can end flush with the surface of the battery, but it can also protrude from or be recessed into the surface of the battery. A coolable battery system includes at least one such battery and a second heat exchanger element for each battery that can be reversibly brought into thermal operative contact with the first heat exchanger element. A method for cooling such a battery in the coolable battery system, in which the first heat exchanger element of the at least one battery is brought in thermal operative connection with the second heat exchanger element, includes maintaining the second heat exchanger element at a lower temperature level than the first heat exchanger element.