A fuel injector, in particular a fuel injector for fuel systems of internal combustion engines, has a piezoelectric or magnetostrictive actuator, a valve needle operated by the actuator by way of a hydraulic temperature compensation device, and a valve closing body operated by the valve needle and cooperating with a valve seat face to form a scaling seat. The temperature compensation device includes a needle driving sleeve which surrounds a valve needle shoulder of the valve needle and, together with a needle driving shoulder, surrounds the valve needle in sections. In addition, the needle driving sleeve together with the valve needle encloses a temperature compensation space, and the temperature compensation space is connected to a fuel inlet of the fuel injector through a directional valve for filling the temperature compensation space with fuel.