Heterogeneous nanostructures have attracted tremendous interest because of their exceptional properties and promising applications in extensive fields. In this work, we employed molecular dynamics (MD) simulations to investigate thermally driven structural and shape evolutions of Pd-Au heterostructured nanorods consisting of hexagonal close-packed (hcp) Pd-core/Au-shell structures in the middle and face-centered cubic (fcc) Au terminated at both ends (referred to as fcc-2H-fcc Pd@Au nanorods). Our results reveal that these nanorods exhibit a two-stage melting mode, that is, melting initiates at both ends of the nanorods and extends to the middle with increasing temperature. Moreover, specific thermodynamic behaviors are associated with the core size. With the lowering core size, the difference in the melting points between the core and the shell in the nanorods decreases accordingly, and the two-stage melting characteristic tends to be obscure. During heating, these nanorods experience a significant shrinkage after the melting of Au at both ends, forming a liquid-like shell/solid-core structure prior to the overall melting. However, two-stage melting is absent in fcc-2H-fcc Au nanorods. These results extend the fundamental understanding of the thermal stability of metallic heterostructured nanorods and provide a theoretical reference for the design and application of one-dimensional metallic heterostructures.