In the paper, the numerical study of a thin layer of a viscous incompressible fluid followed by a co-current gas flow is conducted. The liquid flows on an inclined non-uniformly heated solid surface under the action of gravity. The classical convection equations and the generalized kinematic, dynamic, and energy conditions on thermocapillary boundary are used as a mathematical model. Conditions can be significantly simplified due to parametric analysis of the equations for thermocapillary boundary. The evolution equation derived from the kinematic condition determines the liquid layer thickness change. A numerical algorithm for evaluation of the liquid layer thickness is proposed. Results of numerical simulation of the film motion are presented for the system with ethanol liquid under the action of a nitrogen stream. A comparison of results of numerical simulation based on equations of Oberbeck-Boussinesq and Navier-Stokes equations, and heat transfer is demonstrated. The influence of solid surface incidence angle and solid surface heating conditions on liquid layer flow particularities is investigated.