Determining the boundary conditions of heat transfer in steel manufacturing is a very important issue. The heat transfer effect during contact of two solid bodies occurs in the continuous casting steel process. The temperature fields of solids taking part in heat transfer are described by the Fourier equation. The boundary conditions of heat transfer must be determined to get an accurate solution to the heat conduction equation. The heat flux between the tool and the object processed depends mainly on temperature, pressure and time. It is very difficult and complicated to accomplish direct identification and determination of the boundary conditions in this process. The solution to this problem may be the construction of a process model, performing measurements at a test stand, and using numerical methods. The proposed model must be verified on the basis of parameters which can easily be measured in industrial processes. One of them is temperature, which may be used in inverse methods to determine the heat transfer coefficient. This work presents the methodology for determining the heat flux between two solid bodies staying in contact. It consists of two stages – the experiment and the numerical computation. The problem was solved by using the finite element method (FEM) and a numerical program developed at AGH University of Science and Technology in Krakow. The findings of the conducted research are relationships describing the value of the heat flux versus the contact time and surface temperature.