Inspired by the thermoregulation of mammals via perspiration, cooling strategies utilizing continuously fed evaporating droplets have long been investigated in the field, yet a comprehensive modeling capturing the detailed physics of the internal liquid flow is absent. In this study, an innovative computational model is reported, which solves the governing equations with temperature-dependent thermophysical properties in an iterative manner to handle mass and heat transfer coupling at the surface of a constant shape evaporating droplet. Using the model, evaporation from a spherical sessile droplet is simulated with and without thermocapillarity. An uncommon, nonmonotonic temperature variation on the droplet surface is captured in the absence of thermocapillarity. Although similar findings were reported in previous experiments, the temperature dip was attributed to a possible Marangoni flow. This study reveals that buoyancy-driven flow is solely responsible for the nonmonotonic temperature distribution at the surface of an evaporating steadily fed spherical water droplet.