This paper considers the steel reheating process, in which cold slabs are reheated to a temperature suitable for hot rolling operations. Temperature uniformity within the slab is very important during reheating, as non-uniformities often lead to quality concerns in the later stages of the production process. Attaining slab temperature uniformity is quite challenging, therefore, a thorough understanding of the reheating process becomes very important. Due to the extreme conditions inside the furnace, numerical tools like computational fluid dynamics are necessary for such situations. However, when applied to these complex installations, it often leads to very lengthy computational times. This paper develops a computationally efficient transient model to simulate the environment around a slab. This Truncated Transient Slab Model is a coupled model: it uses the temperature and flow profiles from a full-scale steady-state simulation and imposes those on a smaller domain that represents the immediate environment around the slab. The efficiency of the model is compared to the state of the art. With the simulations available in the literature, it was found that the proposed model can simulate a furnace seven times larger (grid size), with much higher grid and time resolutions, using only a third of the computational resources.