Cell connector for electrically connecting a first cell and a second cell in parallel with each other wherein each of the cells has a hollow cylindrical housing, wherein the housing has an outer casing, an inner casing, a first cap and a second cap, wherein on the one hand the inner casing and the first cap form a first electrical cell conductor and on the other hand the outer casing and the second cap form a second electrical cell conductor and wherein the inner casing has, on the one hand, a first socket on the first cap and, on the other hand, a second socket on the second cap, characterized in that the cell connector has a first electrical connecting conductor, a second electrical connecting conductor and a connecting insulator, that the cell connector is designed to be arranged between one of the caps (6, 7) of the first cell and one of the caps (7, 6) of the second cell, that, on the one hand, the first electrical connecting conductor and the connecting insulator and, on the other hand, the second electrical connecting conductor and the connecting insulator are connected to one another, so that the first electrical connecting conductor and the second electrical connecting conductor are electrically insulated from one another, that the first electrical connecting conductor has a first plug and a second plug, that the first plug is designed to complement one of the sockets (10, 11) of the first cell and the second plug is designed to complement one of the sockets (11, 10) of the second cell, that the first electrical connecting conductor is designed to electrically connect the socket (10, 11) of the first cell and the socket (11, 10) of the second cell to one another, that the second electrical connecting conductor is designed to electrically connect the second electrical cell conductor of the first cell and the second electrical cell conductor of the second cell to one another, and that the first electrical connecting conductor including the first plug and the second plug is designed to receive a medium for temperature conditioning of cells. wherein each of the cells has a hollow cylindrical housing, wherein the housing has an outer casing, an inner casing, a first cap and a second cap, wherein on the one hand the inner casing and the first cap form a first electrical cell conductor and on the other hand the outer casing and the second cap form a second electrical cell conductor and wherein the inner casing has, on the one hand, a first socket on the first cap and, on the other hand, a second socket on the second cap, characterized in that the cell connector has a first electrical connecting conductor, a second electrical connecting conductor and a connecting insulator, that the cell connector is designed to be arranged between one of the caps (6, 7) of the first cell and one of the caps (7, 6) of the second cell, that, on the one hand, the first electrical connecting conductor and the connecting insulator and, on the other hand, the second electrical connecting conductor and the connecting insulator are connected to one another, so that the first electrical connecting conductor and the second electrical connecting conductor are electrically insulated from one another, that the first electrical connecting conductor has a first plug and a second plug, that the first plug is designed to complement one of the sockets (10, 11) of the first cell and the second plug is designed to complement one of the sockets (11, 10) of the second cell, that the first electrical connecting conductor is designed to electrically connect the socket (10, 11) of the first cell and the socket (11, 10) of the second cell to one another, that the second electrical connecting conductor is designed to electrically connect the second electrical cell conductor of the first cell and the second electrical cell conductor of the second cell to one another, and that the first electrical connecting conductor including the first plug and the second plug is designed to receive a medium for temperature conditioning of cells.