In this paper, fluid flows in a thin layer, flowing down an inclined nonuniformly heated substrate, are studied. Mathematical modeling of the fluid flows is carried out on the basis of the long-wave approximation of the equations. In the present case, the basis of the mathematical model is the classical convection equations and equations on a thermocapillary interface. The last equations are a generalization in the case of evaporation at the interface of kinematic, dynamic, and energetic conditions. The parametric analysis of these conditions is performed. Values of characteristic scales and dimensionless parameters of different pairs of "liquid – gas" systems like "ethanol  – nitrogen", "HFE7100 – nitrogen", "FC72 – nitrogen" are presented. The one-sided mathematical model of flows in a thin liquid layer flowing down an inclined wall is presented in the paper in the two-dimensional case for moderate Reynolds numbers. An evolution equation for the layer thickness is derived. It takes into account effects of gravitation, capillarity and thermocapillarity, viscosity and evaporation, and also an action of additional tangential stresses of an external gas phase.