A steam blast box for applying steam to a web of paper conducted over a roll of a paper machine. The box has a closed steam blast chamber which extends along the roll transverse to the direction of travel of the web and to which steam can be fed. The front wall of the box, which faces the roll, has a plurality of steam outlet openings. A steam propagation space is formed between the front wall of the steam blast box and the roll. For controlling the temperature and/or for regulating the amount of heat transferred to the web of paper in the steam propagation space, an air outlet channel, which extends transverse to the direction of travel of the web and is located at the web inlet end of the steam propagation space, is provided for the admixing of air in the steam. In this way, sensitive separate, zone-wise control of the heating of the paper web can be obtained. The steam propagation space can be cooled zone-wise by feeding air on the inlet side. Air and steam are drawn off at the outlet end of the propagation space, also zone-wise across the web.