This study investigates the effect of heat conduction through the support fiber on a droplet's evaporation in a weakly convective flow. Experimentally, a droplet of n-heptane or n-hexadecane with an initial diameter of 700 or 1000 mum was suspended at the tip of a horizontal or vertical quartz fiber (diameter 50, 150, or 300 mum) to evaporate in an upward hot gas flow (at 490 or 750 K). A simple one-dimensional model of transient conduction is formulated in combination with evaporation of the droplet, The calculations agree well with the experiments. In general, heat conduction through the fiber enhances evaporation, with a stronger effect for a lower gas temperature and a thicker fiber. However, the total heat inputs are attenuated when the fiber's diameter is 300 mum. Orientation of the fiber is unimportant. Also, the evaporation rate is enhanced in an oxygen-containing gas flow, due to the additional heating from oxidation around the droplet.