This paper deals with the heat transfer analysis in a welding process: A method is developed to determine the shape of the three-dimensional (3-D) phase change front and to estimate the temperature field within the solid part of the work piece. The problem is formulated and solved as an inverse phase-change problem by using an optimization method. The direct problem is solved in the torch frame and so formulated as an Eulerian approach. The interface between the weld pool and the solid region is parameterized by Bezier surfaces. The most important feature of the presented approach is that the liquid-solid interface as well as the temperature distribution within the solid region can be obtained from additional temperature data available in the solid region, without considering heat transfer and fluid flow in a molten zone. The estimate of these thermal characteristics then allows a thermomechanical calculation of the welded joint (calculation of the deformations and residual stresses). The validity of the numerical solution of the inverse problem is checked by comparing the results with the direct solution of the problem.