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An investigation is performed of heat transfer in films of water and FC-72 liquid falling down a 60×120 mm heater. Heat transfer mode maps are constructed. Zones of structure formation and regions of emergence of breakdown of liquid film are identified, as well as regions of boiling in jets. An averaged coefficient of heat transfer was used in analyzing the experimental data. It is demonstrated that thermocapillary forces have a complex and ambiguous effect on heat transfer. The emergence of extensive stable dry spots causes a decrease in the average coefficient of heat transfer. On the other hand, an increase in the path length of film and in the amplitude of wave motion leads to the washing out of the dry spots and to an increase in the relative intensity of heat transfer. The regularities of heat transfer in the region of flow of film with breakdowns for weakly and intensely evaporating liquids differ significantly. An enhancement of heat transfer is observed under conditions of significant evaporation during structure formation in the thermocapillary mode.