A cooling air supply device for a motor vehicle has a motor vehicle body with an underbody and a unit. The cooling air supply device configured to receive cooling air in the form of an air flow which flows along the underbody counter to the direction of travel, and configured to be self-regulating. The cooling air supply device having a molded part, which is pivotable about an axis of rotation, has an outer surface facing away from the underbody, and has a convex curvature relative to the underbody. A flow duct is between the underbody and the molded part, the flow duct being configured to allow the air flow to be conducted to the unit.