Heating device (11, 111) having: - a carrier (13, 113) which is electrically insulating on an upper side and heats an adjoining medium on an underside, - a heating conductor (23, 123a, 123b) on the carrier (13, 113), - a sensor layer (17, 117) of dielectric material on the carrier (13, 113), wherein the sensor layer - is arranged above or below the heating conductor and is electrically insulated against the heating conductor, - has a temperature-dependent electrical conductivity, and an electrical resistance of the sensor layer changes depending on the temperature at the sensor layer, - a control device and an evaluation device to register the temperature at the carrier (13, 113), wherein the evaluation device is designed to register any change in a control signal (U A) at the sensor layer (17, 117) depending on a temperature and/or on the temperature-dependent electrical conductivity of the sensor layer, characterized in that - the control device is designed to generate the control signal (U A) with alternating current, - the heating device (11, 111) has a transformer with a primary side and a secondary side, - the primary side is connected to the control device and to the evaluation device, - the secondary side has a first connection and a second connection, - the first connection and the second connection are connected in different manner to the heating conductor (23, 123a, 123b), to an electrically conductive sensor electrode (19, 119) or to the carrier (13, 113), - the carrier is electrically conductive in the event that one of the two connections is connected to it, - the two connections are connected on both sides of the sensor layer (17, 117), - on the primary side, a voltage divider of series resistor (R v) and primary side is connected to the control signal (U A), - the evaluation device is connected between the series resistor (R v) and the primary side. - a carrier (13, 113) which is electrically insulating on an upper side and heats an adjoining medium on an underside, - a heating conductor (23, 123a, 123b) on the carrier (13, 113), - a sensor layer (17, 117) of dielectric material on the carrier (13, 113), wherein the sensor layer - is arranged above or below the heating conductor and is electrically insulated against the heating conductor, - has a temperature-dependent electrical conductivity, and an electrical resistance of the sensor layer changes depending on the temperature at the sensor layer, - is arranged above or below the heating conductor and is electrically insulated against the heating conductor, - has a temperature-dependent electrical conductivity, and an electrical resistance of the sensor layer changes depending on the temperature at the sensor layer, - a control device and an evaluation device to register the temperature at the carrier (13, 113), wherein the evaluation device is designed to register any change in a control signal (U A) at the sensor layer (17, 117) depending on a temperature and/or on the temperature-dependent electrical conductivity of the sensor layer, characterized in that - the control device is designed to generate the control signal (U A) with alternating current, - the heating device (11, 111) has a transformer with a primary side and a secondary side, - the primary side is connected to the control device and to the evaluation device, - the secondary side has a first connection and a second connection, - the first connection and the second connection are connected in different manner to the heating conductor (23, 123a, 123b), to an electrically conductive sensor electrode (19, 119) or to the carrier (13, 113), - the carrier is electrically conductive in the event that one of the two connections is connected to it, - the two connections are connected on both sides of the sensor layer (17, 117), - on the primary side, a voltage divider of series resistor (R v) and primary side is connected to the control signal (U A), - the evaluation device is connected between the series resistor (R v) and the primary side. - the control device is designed to generate the control signal (U A) with alternating current, - the heating device (11, 111) has a transformer with a primary side and a secondary side, - the primary side is connected to the control device and to the evaluation device, - the secondary side has a first connection and a second connection, - the first connection and the second connection are connected in different manner to the heating conductor (23, 123a, 123b), to an electrically conductive sensor electrode (19, 119) or to the carrier (13, 113), - the carrier is electrically conductive in the event that one of the two connections is connected to it, - the two connections are connected on both sides of the sensor layer (17, 117), - on the primary side, a voltage divider of series resistor (R v) and primary side is connected to the control signal (U A), - the evaluation device is connected between the series resistor (R v) and the primary side.