A comparative analysis of thermally induced structural transitions in silver nanoclusters, the number of atoms of which corresponded to the “magic” numbers of the icosahedral (Ih) structure with variation of their initial morphology, was carried out by the molecular dynamics method using the modified tight-binding potential TB-SMA. It is shown that, in the case of the initial fcc phase, the formation of the Ih modification, depending on the particle size, occurred either at the stage of preliminary thermal relaxation or during further heating. At the initial amorphous morphology, the nature of the structural transitions underwent significant changes. Thus, even in the case of Ag55 clusters, the icosahedral structure was formed only in 50-60% of the experiments performed. Based on the data obtained, it was concluded that to create a stable Ih structure, it is necessary to use the thermal cycling procedure.