Melting of nanoalloys originates from the alloy surface and gradually propagates into the interior region. The thermal stability of Li cores and Cu shells nanoalloy with size of 3.5 nm is studied through molecular dynamics and embedded atom method with the use of potential energy, Lindemann index, and radial distribution function. Results show that the shell and core Li atoms are melted in two steps: first, some Li atoms in the core migrate to the nanoalloy surface and maintain a typical solid state despite that the system temperature is higher than the bulk melting point of Li because of Li solidification in the solidliquid interface; second, the shell and core Li atoms are simultaneously melted at high temperatures. A comparative study of Li@Cu nanoalloys with different Li atomic numbers shows that thermal stability is enhanced with the decreasing number of Li atoms within the nanoalloys because of weak binding for Cu thin shells.