This final work discusses numerical modelling of the thermal problems using the finite element method. At the beginning, the needed equations and methods for the numerical modelling of the thermal problems in general are explained. In addition, we presented the analysis of the stationary heat transfer problem in steps. This is followed by the comparison of the results of our own computer code with the results, which we got from the use of the Abaqus computer code. In the second part of the final work we used the finite element method for the heat analysis of adding the material with melting. We presented and evaluated two methods of numerical modelling of adding the material in the Abaqus computer code.