In this work, we performed a Monte Carlo simulation study on the thermal evolution of icosahedral Pd-55, Pd43Pt12, and Pd13Pt42 clusters supported on the MgO(100) surface, using the second-moment approximation of the tight-binding potentials for the metal-metal interactions and the many-body potential energy surface for the metal-MgO(100) interaction. The potential energy surface here is obtained by fitting to ab initio calculation results (Vervisch, W.; Mottet, C.; Goniakowski, J. Phys. Rev. B 2002, 65, 245411). The solid-solid structural transformation from the icosahedral structure to the layered fcc structure is found for the Pd-55, Pd43Pt12, and Pd13Pt42 clusters supported on the MgO(100) surface, determined by the changes of the total potential energies and variations of the deformation parameters. It is found that the supported Pd-55, Pd43Pt12, and Pd13Pt42 clusters possess the layered epitaxial fcc structure at higher temperatures after structural transformation. In addition, the composition effect on the transition temperatures of free and MgO(100)-supported Pd-Pt bimetallic clusters is discussed.