The two-dimensional, unsteady, laminar conservation equations for mass, momentum, energy and species transport in the gas phase and mass, momentum and energy in the liquid phase are solved simultaneously in spherical coordinates in order to study heating and vaporization of a droplet entrained in the oscillating flow. The numerical solution gives the velocity and temperature distribution in both gas and liquid phase as a function of time. When the gas flow oscillates around an vaporizing droplet, the liquid flow circulates in the clockwise or counterclockwise direction and the temperature distribution in the liquid phase changes its shapes, depending on the gas fow direction. When the gas flow changes its direction of circulating liquid flow is opposite to the gas flow, forming two vortex circulating in the opposite direction. During the heating period, the difference in the maximum and minimum temperature is large, followed by the almost uniform temperature slightly below the boiling temperature. The mass and heat transfer from the droplet depend on the droplet temperature, droplet diameter and the magnitude of relative velocity, giving the droplet lifetime different from the d$^{2}$-law.