In the heating device, PTC heating elements arranged between current rails lying opposite each other are used, which are fed with supply current from a control electronics unit via the current rails. Metallic heating rib structures are respectively coupled to one of the current rails via an electrically insulating but thermally conducting coupling layer. The air to be heated flows through the heating rib structures which have an undulating shape. The metallic heating rib structures are electrically connected to vehicle ground and thus form a shield that eliminates emissions of electromagnetic interfering radiation without impeding the flow of air.