An electric auxiliary heating unit for a motor vehicle reliably avoids temperature overshoots of the heated air, especially during acceleration phases of the vehicle. The temperature of adjustment the discharged hot air is adjusted in dependence upon the vehicle speed. This is preferably done via a stored characteristic field via which a plurality of vehicle parameters, such as the vehicle speed, the opening condition of the convertible top, the outside temperature, etc., can easily be taken into account. The temperature of the incoming air can also be derived from temperature values which are already available in the vehicle. This heating can preferably be used locally in the vehicle, e.g. in the vehicle seat or in the rear of the passenger compartment. Temperature fluctuations in the heated air can be avoided reliably and easily even in the case of dynamically varying operating conditions of the motor vehicle.