In this paper we experimentally examine evaporation flux distributions and modes of interfacial energy transport for continuously fed evaporating spherical sessile water droplets in a regime that is relevant for applications, particularly for evaporative cooling systems. The contribution of the thermal conduction through the vapor phase was found to be insignificant compared to the thermal conduction through the liquid phase for the conditions we investigated. The local evaporation flux distributions associated with thermal conduction were found to vary along the surface of the droplet. Thermal conduction provided a majority of the energy required for evaporation but did not account for all of the energy transport, contributing 64±3%, 77±3%, and 77±4% of the energy required for the three cases we examined. Based on the temperature profiles measured along the interface we found that thermocapillary flow was predicted to occur in our experiments, and two convection cells were consistent with the temperature distributions for higher substrate temperatures while a single convection cell was consistent with the temperature distributions for a lower substrate temperature.