A cooling device for an electrical energy store, having a heat sink for arranging on one side of a cell assembly formed of energy storage cells of the electrical energy store and for cooling the energy storage cells is provided. The heat sink has openings for aligned arrangement so as to form degassing elements of the energy storage cells. The openings form a degassing duct for a hot gas of the energy storage cells that leaks via the degassing elements. The cooling device has intermediate cooling elements for arranging in clearances of the cell assembly between the energy storage cells in order to compensate for a loss of cooling surface that results from the openings of the heat sink. The intermediate cooling elements are arranged on the heat sink and are designed to dissipate waste heat from the energy storage cells to the heat sink.