Particle transport and turbulence modification in an unstably stratified, particle-laden turbulent flow within a horizontal channel is studied via direct numerical simulations combined with Lagrangian point‒particle tracking techniques. Two-way coupling in momentum and energy is considered in dilute gas‒solid flows under mixed convection (synergistic effects of shear and buoyancy). For comparison, simulations of neutral turbulence are also conducted with equivalent parameters. The study reveals that large-scale longitudinal vortical structures induce significant spatial heterogeneity in the spanwise distribution of inertial particles. This heterogeneity is characterized by an increase in the particle concentration on the side of the cold plume and a corresponding decrease on the side of the hot plume. In the context of unstably stratified turbulence, particles reduce the fluid streamwise velocity and promote its profile toward symmetry. This phenomenon contrasts with that observed in neutral flows, where particles induce velocity asymmetry by dragging the upper flow and accelerating the lower flow. A quantitative analysis of the heat flux indicates that particles absorb heat as they settle, thereby reducing the average temperature of the flow. Buoyancy effects slow the settling and reinjection of particles, which in turn diminishes thermal energy absorption. Particles with higher inertia preferentially settle on the cooler plume side, minimizing their participation in heat exchange due to prolonged durations of repeated wall collisions.