A radar antenna device (16) having an antenna arrangement (19) that is accommodated in a housing (17) and is provided with a protective plate (20) for being separated with respect to a furnace atmosphere formed within a furnace chamber, said protective plate (20) being disposed on the housing, a radar-transparent limp material layer (21) comprising pores being disposed as a shield at a distance upstream of the protective plate (20) in such a manner that a space which is separated by the material layer (21) with respect to the furnace chamber is formed, a fluid line opening into said space for applying a fluid flow to the material layer (21).