This work is focused on the development of computational algorithms to create a simulator for solving the heat transfer during the continuous casting process of steel. The temperatures and the solid shell thickness profiles were calculated and displayed on the screen for a billet through a defined continuous casting plant (CCP). The algorithms developed to calculate billet temperatures, involve the solutions of the corresponding equations for the heat removal conditions such as radiation, forced convection, and conduction according to the billet position through the CCP. This is done by a simultaneous comparison with the kinematics model previously developed. A finite difference method known as Crank-Nicholson is applied to solve the two-dimensional computational array (2D model). Enthalpy (H_I,J) and temperature (T_I,J) in every node are updated at each step time. The routines to display the results have been developed using a graphical user interface (GUI) in the programming language C++. Finally, the results obtained are compared with those of industrial trials for the surface temperature of three steel casters with different plant configurations in different casting conditions.