Evaporation of water droplets on a structured surface is studied experimentally. With an increase in the wall temperature Tw from 28-70°С the exponent n increases from 1-1.37 in the evaporation law (j = dm/dt ~ R0n, where m is the droplet mass and R0 is the droplet radius). Usually, researchers simulating droplet evaporation consider a linear relationship between the evaporation rate, j, and the droplet radius, R0 (n = 1). This paper shows an increase of the exponent, n, with a growth of the wall temperature, Tw. The diffusion vapor layer on the droplet interface and the boundary air layer on the surface of the heated cylinder with a diameter exceeding the droplet’s one are formed. A neglect of free convection more than five times underestimates calculation results compared with experimental data. At droplet evaporation it is necessary to take into account convection in a vapor-gas medium and wall roughness.