Single impurity effect on the melting process of magic number Lennard-Jones, rare gas, clusters of up to 309 atoms is studied on the basis of Parallel Tempering Monte Carlo simulations in the canonical ensemble. A decrease on the melting temperature range is prevalent, although such effect is dependent on the size of the impurity atom relative to the cluster size. Additionally, the difference between the atomic sizes of the impurity and the main component of the cluster should be considered. We demonstrate that solid-solid transitions due to migrations of the impurity become apparent and are clearly differentiated from the melting up to cluster sizes of 147 atoms.