The 1D confinement of electrons within quantum wells produces a set of new states, the quantum well states (QWS), which may influence substantially the electronic energy and, thus, the total energy of the system. Pb grown on Cu(111) shows these effects in the form of "magic heights" for the 3D nanoislands that appear upon deposition at 300K.@footnote 1@ The "magic heights" are equivalent to the "magic numbers" reported for clusters, He droplets or nuclei. Deposition of Pb at 60 K, however, produces flat, metastable films that cover uniformly the Cu substrate. Their thicknesses can be determined by the characteristic energy of the QWS measured with Tunnelling Spectroscopy. The films grow layer by layer at low temperatures because of kinetic constraints, but upon heating, they decompose into the heights more stable. The dynamics of the thermal evolution of films of different thicknesses is explored by movies recorded with a Variable Temperature STM and compared to electronic energy calculations. We find that each Pb thickness becomes unstable at a different temperature (with films with QWS at the Fermi level (such as 9 ML-thick) being particularly unstable), while layers with thickness corresponding to "magic heights" are more stable. Some thicknesses are particularly stable, giving rise to atomically flat films of Pb over micron scales even at room temperature. @FootnoteText@@footnote 1@R. Otero, A.L. Vazquez de Parga and R. Miranda, Phys. Rev. B 55, 10791 (2002).