The work is devoted to the justification of the use of rheological constitutive relation fluid polymer media prepared on the basis of the molecular-kinetic concepts of the dynamics of polymer chains, taking into account the heat transfer. The relevance of this work is the fact that the task of formulation of equations systems suitable for the flows of melts of linear polymers, still does not have a unique solution, and therefore all of the proposed rheological constitutive relations require justification. As the author of the original model was chosen new rheological model (modified Vinogradov and Pokrovskii model). On the model basis the task of forming a melt of the polymer film was examined. This was the starting point for the construction of a mathematical model of the film forming polymer melt. It was observed the appearance of a "neck" when the calculation according to the half-width of the film to the distance from the spinneret exit. The very mathematical model of a melt molding is recorded in the one-dimensional approximation, which makes it suitable for engineering calculations. On the basis of studies of the effect of dimensionless parameters of the model for the type of dependencies obtained by the author concluded that the applicability of this approach to the description of characteristics of the resulting films. This problem is a test in the calculation of two-dimensional and three-dimensional flows of viscoelastic fluids.