The position of a rail vehicle that is parked on a track is monitored in a cold movement detection. A vehicle-side device of an automatic train safety system is deactivated when the vehicle is parked. Prior to the deactivation, a first positional value is determined by the automatic train safety system, and independently, a second positional value is determined by another localization system. With the vehicle-side device deactivated, the actual position of the vehicle is monitored by the other localization system. The additional positional values and/or a deviation of the actual position from a target position is transmitted to a track-side device of the train safety system. When the vehicle-side device is activated, the track-side device transmits the actual position of the vehicle to the vehicle-side device. If the vehicle has not moved, the automatic train guidance system can immediately assume the monitoring process starting from the first position.