The local evaporation rate and interfacial temperature are two quintessential characteristics for the study of evaporating droplets. Here, it is shown how one can extract these quantities by measuring the vapor concentration field around the droplet with digital holographic interferometry. As a concrete example, an evaporating freely receding pending droplet of 3M Novec HFE-7000 is analyzed at ambient conditions. The measured vapor cloud is shown to deviate significantly from a pure-diffusion regime calculation, but it compares favorably to a new boundary-layer theory accounting for a buoyancy-induced convection in the gas and the influence upon it of a thermal Marangoni flow. By integration of the measured local evaporation rate over the interface, the global evaporation rate is obtained and validated by a side-view measurement of the droplet shape. Advective effects are found to boost the global evaporation rate by a factor of 4 as compared to the diffusion-limited theory.