Molecular dynamics simulations have been employed to explore the melting behavior of nanometersized Pb particles encapsulated in spherical and polyhedral fullerene cages of suitable size. The encapsulated particles, as well as the corresponding unsupported ones for comparison, were submitted to a gradual temperature rise. Encapsulation is shown to severely affect the thermodynamic behavior of Pb particles due to the different thermal expansion coefficients of particles and cages. This determines a volume constraint that induces a rise of pressure inside the fullerene cages, which operate for particles as rigid confinement systems. The result is that surface pre-melting and melting processes occur in encapsulated particles at temperatures higher than in unsupported ones.