In the paper, a mathematical model is developed to describe thin liquid layer flows on an inclined, nonuniformly heated surface. Mathematical modeling is performed with the use of the Navier- Stokes equations for a viscous incompressible liquid and equations obtained by generalization of kinematic, dynamic, and energetic conditions on a free boundary for the case of a mass transfer due to evaporation. A long-wave approximation of the Navier-Stokes equations, heat transfer equation, and equations of the conditions on the interface allows a mathematical model to be elaborated for studying thermocapillary flows with evaporation. A parametric analysis of the generalized kinematic, dynamic, and heat equations on the interface with evaporation is carried out. The mathematical model of thin liquid layer flows on the inclined surface is presented in a two-dimensional case for large values of the Reynolds number. The problems are solved for the zeroth and first orders of approximations of expansion terms in powers of a small parameter. An evolution equation of the layer thickness is derived that takes into account the effects of gravitation, capillarity, thermocapillarity, viscosity and evaporation alongside with an action of additional tangential stresses of the co-current gas flow.