The paper presents the results of experimental and numerical studies of boiling heat transfer in the flow of refrigerants R123 and R11 through vertical, rectangular minichannels, with one wall heated. An application of liquid crystal thermography has helped detect two-dimensional temperature distribution on the heating surface, allowing determination of boiling heat fluxes and experimental boiling curves. The main objectives of the paper included the development of two-dimensional approach to solve the inverse heat conduction boundary problem for determining local values of internal heating surface temperature, boiling heat flux and heat transfer coefficient, and the improvement of the applied numerical method making use of the equalizing calculus and heating surface temperature measurement errors. A detailed discussion of temperature, heat flux and heat transfer coefficient errors is also provided.