In the work, a mathematical description of thermal processes in laser welding with the use of the classical theory of thermal conductivity was performed. The thermal cycle under the action of radiation on the surface was analyzed using the models of overall heat balance, distributed surface, point, circular and linear heat sources. The modeling of welding process consisted in solving the problem of forming thermal fields in viscoelastic polymer materials at a moving inner heat source. It was assumed that the upper part is transparent to laser radiation and the lower one has a set coefficient of light beam absorption, and their thermophysical characteristics depend on temperature. The equations of thermal conductivity and defining equations were formulated, supplemented by the boundary conditions of convective heat transfer and the initial temperature distribution. For the numerical implementation of certain equations the finite element method was used, which is based on an alternative formulation of the problem. The results of mathematical modeling showed the peculiarities of the formation of thermal fields in the transmission laser welding of polymer films at different parameters of welding mode.