An energy storage device is provided with at least one energy storage unit (1). The energy storage unit (1) comprises a thermal storage element (3) made of a solid material and an electrical heating device (5) for heating the thermal storage element (3). According to a first concept, the electrical heating device (5) is adapted to heat the thermal storage element (3) by means of generating an electric current within the material of the thermal storage element (3). According to a second concept, an electric gas insulation (8) is provided, in order to electrically insulate the electrical heating device (5) from the thermal storage element (3). Furthermore, a method for storing energy by means of such an energy storage device is provided.