While traditional thermodynamic equilibrium requires uniform temperature across coexisting phases, underdamped active matter systems can sustain nonequilibrium hot-cold coexistence through motility-induced phase separation. We investigate particle demixing and emergent temperature gradients in binary mixtures of inertial active and passive particles. Remarkably, within specific parameter ranges of intermediate particle inertia and self-propulsion strength, the system simultaneously achieves pronounced particle demixing and sustains significant hot-cold coexistence. Activity differences drive rapid species separation, which is further enhanced over time by persistent rotational diffusion. The synergy between inertia and activity significantly amplifies temperature differences both between particle species and across coexisting gas-liquid phases. These temperature disparities originate from inertia-enabled energy storage, collision-mediated energy transfer, propulsion-driven acceleration, and weakened liquid-phase cohesion. Unlike equilibrium systems, active-passive mixtures circumvent thermal homogenization by maintaining kinetic temperature gradients through continuous energy injection and dissipation. These findings elucidate fundamental principles of nonequilibrium self-organization in hybrid systems, with implications for bio-inspired materials, microbial ecology, and energy transport in active composites.

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• Active Brownian particles
• Dry active matter