An electrochemical energy accumulator apparatus according to the invention has at least one galvanic cell. Furthermore, the electrochemical energy accumulator apparatus has at least one diverting device which is assigned to the at least one galvanic cell, and at least one connecting device which is assigned to the at least one diverting device. The electrochemical energy accumulator apparatus is characterized in that the at least one connecting device is assigned at least one heat exchanger device, wherein the at least one heat exchanger device is designed to exchange thermal energy with the at least one connecting device.