The occurrence of an Ag layer on top of a Cu (111) substrate can result from either deposition of Ag atoms on a Cu (111) substrate or from strong segregation at the (111) surface of a dilute Cu (Ag) alloy, Quenched molecular dynamics simulations within many-body tight-binding potentials show that two structures compete at T = 0 K. The first one corresponds to a Moire structure built by the superposition of an hexagonal Ag (111) layer on top of a Cu (111) substrate, the lattice parameter of the Ag layer being very near of the bulk Ag one. The second structure involves constitutive vacancies forming a triangular loop of dislocation in the first Cu underlayer. We show here that increasing temperature slightly favours the Moire structure along a free energy criterion, as a result of a complex interplay between internal energy and vibrational entropy. This indicates that the experimentally observed transition between the Moire structure at low temperature and the triangular one at higher temperature has probably a kinetic origin and is not a true equilibrium phase transition.