Thermal stability of core-shell nanoparticles (CSNPs) is crucial to their fabrication processes, chemical and physical properties, and applications. Here we systematically investigate the structural and thermal stabilities of single Au@Ag CSNPs with different sizes and their arrays by means of all-atom molecular dynamics simulations. The formation energies of all Au@Ag CSNPs we reported are all negative, indicating that Au@Ag CSNPs are energetically favorable to be formed. For Au@Ag CSNPs with the same core size, their melting points increase with increasing shell thickness. If we keep the shell thickness unchanged, the melting points increase as the core sizes increase except for the CSNP with the smallest core size and a bilayer Ag shell. The melting points of Au@Ag CSNPs show a feature of non-monotonicity with increasing core size at a fixed NP size. Further simulations on the Au@Ag CSNP arrays with 923 atoms reveal that their melting points decrease dramatically compared with single Au@Ag CSNPs. We find that the premelting processes start from the surface region for both the single NPs and their arrays.