We studied the thermodynamic properties of a large ensemble of polymer crystals confined in the spherical cells of a block copolymer mesostructure. Nucleated only at large supercoolings, the resulting highly imperfect crystallites showed significant reorganization upon heating. A broad melting range is caused by the superposition of sharp melting transitions of the individual crystals, which take place at different temperatures corresponding to a multitude of possible metastable states. Thus, at the limit of their stability, individual nanocrystals only have the choice between complete melting or stabilization by reorganization taking place entirely in the crystalline state. As a consequence of their smallness, melting-recrystallization processes within the individual cells are prohibited.