In the steady-state experiments of water droplet evaporation, when the throat was heating at a stainless steel conical funnel, the interfacial liquid temperature was found to increase parabolically from the center line to the rim of the funnel with the global vapor-phase pressure at around 600 Pa. The energy conservation analysis at the interface indicates that the energy required for evaporation is maintained by thermal conduction to the interface from the liquid and vapor phases, thermocapillary convection at interface, and the viscous dissipation globally and locally. The local evaporation flux increases from the center line to the periphery as a result of multiple effects of energy transport at the interface. The local vapor-phase pressure predicted from statistical rate theory (SRT) is also found to increase monotonically toward the interface edge from the center line, However, the average value of the local vapor-phase pressures is in agreement with the measured global vapor-phase pressure within the measured error bar.