The annealing process of well-defined long truncated decahedral Cu rods of a diameter in the nanometer-size range and a length of the order of 1 micron was studied. For isolated rods on the grid, two melting processes that initiated a drastic change in the melting temperature were observed. These variations are explained in terms of the crystallinity of the nanorods. In the absence of defects, the nanorods are highly stable with a melting temperature close to the bulk phase. In contrast, in the presence of defects, the melting temperature drastically decreases. In this case, nanocrystals can undergo a shape transformation before melting from rod to cylinder.