the fuel metering device 3 meters fuel that is admitted to the fuel injection valves 6 through pressure conduits 5 the fuel injection valves 6 inject fuel into the individual intake tubes 7 of the internal combustion engine in each fuel injection valve 6 there is situated a heater 8 provided with electric conductors 9 and a heat insulation 10 for a good thermal separation of the heater 8 from the surrounding components of the engine the fuel filled space of each fuel injection valve 6 is closed off by a valve needle 11 the opening pressure for which is determined by a closing spring 12 urging the valve needle 11 into its closed position the heat output of the heater 8 is regulated by a control device 13 which receives signals from temperature sensors 14 15 16 17 and from a switch 18 the temperature sensor 14 monitors the maximum fuel temperature in the fuel injection valve 6 downstream of the heater the temperature sensor 15 is responsive to the temperature of the intake air at the location of injection the sensor 16 is responsive to the temperature of the cylinder head while the sensor 17 is responsive to the temperature of the coolant in water cooled engines switch 18 transmits a signal when there is an air flow in the intake manifold and thus indicates whether the engine is running or whether it is at a standstill as the fuel flows through the fuel injection valve 6 the electrical heating body 8 heats it to a temperature at which a preponderant portion of the fuel is.