We used molecular dynamics (MD) simulations with embedded atom method (EAM) potential to investigate the effect of size, simulation temperature heating and cooling rates on the nanoparticle formations, elemental distributions, melting, crystallization and phase transitions in equiatomic Ag-Cu-Ni ternary nanoparticle systems. Five model systems consisting of N = 412, 1348, 3173, 6222 and 10,843 total atoms of pure, metallic, single oriented, spherical silver (Ag), copper (Cu) and nickel (Ni) particles used. A two-step heating process including relaxing and heating with fast, 1 x 10(13) K s(-1) and slow, 1 x 10(11) K s(-1) heating rates applied to monometallic Ag, Cu, Ni and ternary AgCuNi clusters to study melting behavior of systems. We obtained melting temperatures for various systems and found structural and morphological changes depend on the number of atoms in ternary cluster. A four-step thermal process including relaxing, heating, annealing and cooling applied to model systems to study effects of temperature (T = 1000, 1500 and 2000 K) and cooling rates (fast, 1 x 10(13) K s(-1) and slow, 1 x 10(11) K s(-1)) for crystallization. We detected core-shell structure, Ag@CuNi for all simulations because of surface energy. The total energy of ternary clusters decrease linearly with increasing N, revealing similar mechanisms govern for core-shell structure and phase transitions. Energy-Temperature data of slow cooling rate have shown phase transition (crystallization) for monometallic Ag, Cu, Ni and ternary AgCuNi clusters, increasing with N. Fast cooling rate influences energy configuration and result in amorphous phases. Polyhedral template matching method applied to study phase transitions. For slow cooled clusters, face-centered cubic (FCC) and hexagonal close packed (HCP) structures are dominant while for fast cooled clusters, we observed amorphous phases with HCP and icosahedral structures. Furthermore, we used centrosymmetry parameter to identify the origin of the FCC structure. Our data show increasing simulation temperature and decreasing cooling rate favor crystallization of ternary AgCuNi clusters.