The thermal stability of bimetallic nanoparticles plays a crucial role in their performance in applications in catalysis, biotechnology, and materials science. In this study, we employ molecular dynamics simulations to investigate the melting behavior of Au-Pd nanoparticles with cuboctahedral, icosahedral, and decahedral geometries. Using a tight-binding potential, we systematically explore the effects of particle size and composition on the melting transition. Our analysis, based on caloric curves, Lindemann coefficients, and orientational order parameters, reveals distinct premelting behaviors influenced by geometry. Larger particles exhibit a coexistence of a pseudo-crystalline core and a partially melted shell, but, in decahedra and icosahedra, melting of the core occurs unevenly, with twin boundaries promoting the melting of one or two of the tetrahedral subunits before the rest of the particle. Notably, icosahedral nanoparticles display higher thermal stability, while both icosahedral and decahedral structures exhibit localized melting within twin boundaries. Additionally, we generate HAADF-STEM simulations to aid the interpretation of in situ electron microscopy experiments.