The meltinglike transition in unsupported icosahedral Na-N clusters, with N = 135-147, has been studied by isokinetic molecular dynamics simulations based on an orbital-free version of density functional theory. A maximum in the melting temperature, T-m, is obtained for Na-141, while the latent heat, Delta E, and entropy of melting, AS, are maximal for Na-147. These observations are in close agreement with calorimetric experiments on Na-N(+) clusters. The size evolution of Delta S is rationalized by the emergence of important premelting effects associated with the diffusive motion of atomic vacancies at the cluster surface. The precise location of the maximum in T-m is explained in terms of two different thermally activated structural instability mechanisms which trigger the meltinglike transition in the size- ranges N = 135-141 and N = 141-147, respectively.