This paper presents a numerical study of the Tungsten Inert Gas welding process. In this study, a thermo-elastic–plastic model was developed for the purpose of simulating the temperature distribution and stress fields during welding, utilizing the CAST3M finite element calculation code. The initial focus of this study is an investigation of the thermal behavior of an AM60 magnesium alloy part during the TIG welding process. The aim is to predict the temporal evolution of temperature at any given point within the assembly. In order to achieve this objective, the transient heat equation is solved, taking into account the non-linearity caused by the mobile heat source loading and the dependence of thermo-physical parameters on temperature. The boundary conditions, initial condition, and loading are defined based on experimental data. The numerical results are presented in the form of isotherms and temperature vs. time trends, allowing for the tracking of the thermal history of the assembled parts during and after welding. A comparison between selected numerical model results and experimental observations demonstrated good agreement, which validates the numerical determination of the size of the molten zone. Subsequently, the residual stresses generated in the welded parts are also predicted using the thermal history as loading in the mechanical model.