The paper presents a theoretical analysis of a convective fluid flow with a concurrent gas flow accompanied by evaporation at the interface. The analysis of two-layer flows is based on a mathematical model taking into account evaporation at a thermocapillary boundary and effects of thermal diffusion and diffusion heat conduction in the gas–vapor layer. New exact solutions describing steady two-layer flows in a channel with the interface remaining undeformed and examples of velocity and temperature profiles for the HFE-7100 (liquid)–nitrogen (gas) system are presented. The influence of longitudinal temperature gradients along the channel boundaries, the gas flow rate, and the height of the fluid layer on the flow regime and evaporation rate is studied. A comparison of the calculated data with experimental results is performed.