The evaporating water droplets on a horizontal heated substrate were experimentally studied. The constantan foil 25 μm thick with a size of 42×35 mm2 was used as a substrate. The experiments were carried out with a single droplet or with an ensemble of two or three droplets on the foil. The temperature of the lower surface of foil was measured by an IR scanner. To determine the heat flux density at evaporation of liquid near the contact line, the Cauchy problem for the heat conduction equation was solved using the thermographic data. The results of calculations showed that the maximal heat flux density takes place in the region of the contact line and exceeds the average heat flux density from the entire surface of foil. This is explained by the heat inflow from the foil periphery to the droplet due to relatively high value of the coefficient of heat conductivity of the foil material and high evaporation intensity in the contact line region.