In the realm of advanced material science, multi-principal element alloys (MPEAs) have emerged as a focal point due to their exceptional mechanical properties and adaptability for high-performance applications. This study embarks on an extensive investigation of four MPEAs—CoCrNi, MoNbTa, HfNbTaTiZr, and HfMoNbTaTi—alongside key pure metals (Mo, Nb, Ta, Ni) to unveil their structural and mechanical characteristics. Utilizing a blend of molecular statics and hybrid molecular dynamics/Monte Carlo simulations, the research delves into the impact of chemical short-range order (CSRO) and thermal effects on the fundamental structural parameters and stacking fault energies in these alloys. The study systematically analyzes quantities such as lattice parameters, elastic constants (C11, C12, and C44), and generalized stacking fault energies (GSFEs) across two distinct structures: random and CSRO. These properties are then evaluated at diverse temperatures (0, 300, 600, 900, 1200 K), offering a comprehensive understanding of temperature’s influence on material behavior. For CSRO, CoCrNi was annealed at 350 K and MoNbTa at 300 K, while both HfMoNbTaTi and HfNbTaTiZr were annealed at 300 K, 600 K, and 900 K, respectively. The results indicate that the lattice parameter increases with temperature, reflecting typical thermal expansion behavior. In contrast, both elastic constants and GSFE decrease with rising temperature, suggesting a reduction in resistance to stability and dislocation motion as thermal agitation intensifies. Notably, MPEAs with CSRO structures exhibit higher stiffness and GSFEs compared to their randomly structured counterparts, demonstrating the significant role of atomic ordering in enhancing material strength.