Abstract: An electrical energy storage device includes at least one galvanic cell partly surrounded by a cell sheath, at least one heat-conducting device effectively connected to the galvanic cell, the heat-conducting device being suitable for supplying heat energy to the cell and/or conducting heat energy from the cell, a cell holding device enclosing an interior space at least partially with a wall, the interior space being suitable for accommodating each galvanic cell, and the cell sheath being at least partly effectively connected to the wall, at least one first measurement device suitable for acquiring a temperature at a prespecified position of the galvanic cell, and a control device suitable for evaluating a signal of each first measurement device that is present and/or for controlling the heat-conducting devices, heat-conducting apparatus being situated between the cell sheath and at least one of the wall of cell holding device and an additional cell sheath.