A semiconductor device includes a drift structure formed in a semiconductor body. The drift structure forms a first pn junction with a body zone of a transistor cell. A gate structure extends from a first surface of the semiconductor body into the drift structure. A heat sink structure extends from the first surface into the drift structure. A thermal conductivity of the heat sink structure is greater than a thermal conductivity of the gate structure and/or a thermal capacity of the heat sink structure is greater than a thermal capacity of the gate structure.