Thermophysical properties of a liquid have an influence on features of liquid film behavior under heating. Heating of some area of a free surface produces a temperature gradient along that area and a variation of surface tension in that area. In this case, there appears a tangential force directed along the surface tension gradient toward lower temperatures (Marangoni effect). With the properties mentioned above, it is possible to control the film free surface and its thickness. In this paper, we investigate such possibility for the film hanging between two solid walls under microgravity conditions. We develop a mathematical model based on the twodimensional Navier — Stokes equations and the equation of heat conduction. A convective motion of liquid in the film is considered as the motion of the thin layer of viscous non-isothermal liquid while assuming that the liquid is noncompressible and viscous and density are constants. The equations of motion are written in terms of vorticity and flow function. Boundary conditions for the equations are obtained in explicit form. Numerical investigations demonstrate that a thermal load of specified type directed to the film free surface can significantly reduce thickness of a sizeable part of the film length, thus, flattening that part. The results of computational solutions of model problems are presented.