• Local heat transfer coefficient was estimated for thin liquid film evaporation in a capillary tube. • Temperature infrared measurements were employed as input data of the inverse heat conduction problem. • A robust estimation procedure was adopted. • Procedure validation through the application to both synthetic and experimental data. • Original insight of thin liquid film evaporation was given. Two-phase heat transfer devices consisting of mini and microtubes represent a powerful solution to the continuous reduction of electronic components' dimensions and to the increase of the power to dissipate. Despite many studies on the two-phase heat transfer phenomenon in minitubes, most provided outcomes regarding the average heat transfer coefficient or Nusselt number. A technique to assess the local convective wall heat flux and heat transfer coefficient is proposed, validated, and then applied to the experimental case of thin-film evaporation in a heated capillary tube. The evaporation of the thin film of liquid plays a vital part in the two-phase heat transfer phenomenon inside mini/microtubes. Our study investigated this phenomenon by examining a semi-infinite slug flow. The estimation method used is represented by the inverse heat conduction problem solution in the tube wall, applying the Tikhonov regularisation method. The temperature distributions on the outer surface of the channel measured by an infrared camera were employed as input data for the inverse problem. The estimated heat transfer coefficient distributions confirm the available correlations in average values and provide insight into these complex phenomena in local and instantaneous quantities.