Temperature field has an important influence on the phase changes and, finally, on the microstructure and mechanical properties, residual stresses and strains development in the welded joints. During the welding, temperature field shape and its profile depend on many factors but, assuming some assumptions regarding homogeneity and materials isotropy, the mathematical relations for different practical cases can be obtained. Besides, welded bodies can be infinite or semi-infinite as the plates, bars and massive bodies are considered. The instantaneous or permanent thermal sources, fixed or mobile have an important influence on the temperatures distribution. Therefore, the paper presents some analytical solutions for the temperatures prediction in the welded joints in case of the mobile sources with 2D and 3D Gauss distribution