Operation of the soaking pits of the rolling mill is considered. Reconstruction of them has been discussed. It has been shown that convective heat transfer plays important role in operation of the pits. In order to provide efficient heat transfer, physical modeling of operation of the pits has been performed. Results of modeling has made it possible to determine local coefficient of convective heat exchange in model furnace. Mathematical model has been used for calculating the coefficient of convective heat exchange in industrial furnaces on basis of the model coefficients. Results of the calculations have been used for creating the efficient design of the pits.