Abstract Thermodynamics can be understood as the discipline of the physical sciences, that studies theoretically and practically the different manifestations of energy. The study of thermodynamics is important in relation to the understanding of thermal systems in industry, as well as, supporting energetic processes in living organisms. In relation to the study of energy processes in the context of heat transfer, concepts from thermodynamics are relevant. In the present investigation, the process of heat conduction in a metal bar is analyzed by applying the heat equation and the concept of entropy variation. The first part of the research proposes a numerical method to solve the heat equation in addition to a set of finite difference equations describing the energetic behavior of the system. The numerical solution of the heat equation and the thermodynamic behavior of the system are studied by programming to demonstrate the fit of the results with the theoretical models. Finally, applications of the achieved results in engineering contexts are discussed.