At least one vent hole is provided on an aerodynamically constructed covering part for the underside of a motor vehicle. A partial flow of the cold fresh air flows through the vent hole between the covering part and the roadway and is guided to a space which is situated above and accommodates assemblies and/or chassis parts. At least one suction device is provided on the covering part for carrying away the heated air situated in the space disposed above in the direction of the roadway.