The invention provides a process and apparatus for casting and directly rolling casting strands (4) made from steel, preferably thin slab strands, the strands (4) in transferred to a soaking furnace (10), the induction temperature is regulated to the rolling temperature. The temperature compensation can also be operated in high speed. The method comprises equalizing shorter dwell times by intensive differential heating of the longitudinal sections (4b) in the head region (4c) and in the middle region (4d) and by low heating in the foot region (4e) with increasing casting speeds of 3-10 m/min.or during operation of parallel continuous casting devices (15, 16).