Cubic monoatomic nanoframes of Ag, Au, and Pt were modeled in terms of their evolution with temperature. Using an approximate quantum method for the energetics, Monte Carlo atomistic simulations were performed to determine the critical temperatures at which the nanoframe evolves from its original shape to either a cluster of nanoparticles after all sides of the frame are broken, or to a large cluster after collapsing onto its own internal void. The mechanisms by which these two behaviors take place are discussed within the framework of a simple rule which determines the relationship between the structural factors (side and width) that characterize the transition from one to the other.