Using the localized surface plasmon resonance as a probe in solid and liquid Sn nanoparticles of 107 nm diameter and 52 nm height, we have studied their kinetics of melting and freezing at temperature ramps and, for the first time, at fixed temperatures. During temperature ramps, the kinetics exhibit distinct hysteresis. The melting occurs near the bulk melting point while the freezing is observed at much lower temperatures so that the undercooling interval is approximately 130 K. The time scale of the freezing kinetics measured at different fixed temperatures rapidly decreases as the latter are lowered. All these findings have been quantitatively described by assuming the nucleation to occur on the edges of nanoparticles and employing the classical nucleation theory with the corresponding modifications.