The evolution of the roughness exponent of vapor-deposited thin gold films (the object) on smooth glass substrate at 298 K has been observed by scanning tunneling microscopy. This evolution was enhanced by keeping the films at 323 K in contact with aqueous 0.5 M H2SO4 containing different KCl concentrations for 24 h. It implies a decay of the surface roughness for lengths larger than the grain size of the object leading to better ordered surface structures. Results are compared to those obtained during film grown by increasing the temperature of the glass substrate from 298 to 673 K. The analysis of surface roughness data indicated an enhancement of surface atom diffusion in ordering the gold surface structure, by either anion adsorption or deposition temperature.