Many engineering problems involve heat transfer with phase change and their solution often lead to challenging heat transfer problems having no direct solution. A direct solution in this respect means the determination of the thermal behaviour of a system under imposed initial and boundary conditions. The direct solution is not possible in problems where those initial and boundary conditions are unknown. In such cases, an inverse approach has to be used. However, most of the methods available for the solution of inverse heat transfer problems have been applied to heat transfer problems without the phase change. In this respect, soft computing methods seem to be a promising approach. The reason is that soft computing methods build on artificial intelligence, nature-inspired mechanisms and other principles, which enable to effectively find a sufficiently accurate solution to even very complex problems for which hard computing approach fails. In this paper, a computer heat transfer model accounting for the phase change was created and a neural network approach, which also belongs to the soft computing family, was applied to the solution of an inverse heat transfer problem. The identical problem was also solved by means of a well-established (traditional) Beck’s method and the two inverse solutions were compared to each other, including the assessment of the overall computational procedure. The results showed that the approach based on neural networks was efficient and qualitatively led to similar results as in case of the Beck’s method and was computationally more efficient.