Formation of the patterns of catalytically active metal containing droplets on substrates is an important process for the growing Si wire-like crystals because it predetermines the main crystal parameters. Understanding physical mechanisms of droplet evolution during thermal treatments and derivation of associated parameters are the clue to the controlled formation of droplet ensembles and thus to the predicted growing Si wire-like crystals. In this work, the kinetics of the evolution of droplet ensembles on the surface of substrate as a result of coalescence and atom evaporation is studied theoretically. Obtained theoretical results are compared to the experimental data on the evolution of the ensembles of Au/Si droplets on Si substrate formed by rapid thermal anneals of thin gold film in the temperature range from 900 to 1050°C. The activation energy of droplet diffusion on the surface of substrates is estimated.