mill and a final rolling mill neither shown and on which hot steel 2 that has been preliminarily rolled in the preliminary rolling mill is advanced to the final rolling mill in a direction normal to the plane of the figure i e either towards or away from the viewer in accordance with the invention the lateral edge portions of the steel strip 2 are partially covered by heat reflectors which as shown for the reflectors 5 may be of circular arc shape or as shown for the reflector 6 of elliptical arc shape of course both types of shapes can be used along one and the same roller conveyor or only a single shape can be used the lateral edges of the steel strip 2 are surrounded by the reflectors 5 6 at a distance r and towards the center of the steel strip 2 i e the mid point between the two lateral edges the strip is covered still to the extent of approximately r 2 diagrammatically illustrated devices 7 8 already known per se for shifting other elements may be provided in order to shift the reflectors 5 6 towards and away from the lateral edges of the steel strip 2 as indicated.