The evaporation dynamics of stationary water droplets held within an electrodynamic trap are investigated in a nitrogen flow of variable velocity. In particular, the influence of the nitrogen gas flow on the temperature of the evaporating water droplets is studied. By applying a contact free measurement technique, based on spontaneous Raman scattering, time averaged and time resolved measurements of temperature in the droplet volume are compared. This technique determines the temperature from an intensity ratio in the OH stretching band of the Stokes-Raman scattering after calibration. The measured trends in temperature over the first 5 s of evaporation are found to be in agreement with theoretical calculations of the heat and mass transfer rates.