Surfactant-stabilized oil-in-water and water-in-oil emulsions, encompassing a wide range of chemical compositions, exhibit remarkable temperature-controlled sphere-to-icosahedron droplet shape transformations. These transformations are controlled by the elasticity and closed-surface topology of a self-assembled interfacial crystalline monolayer. Since many practical emulsions are synergistically costabilized by both surfactants and colloidal particles, we explore the influence of surface-adsorbed hydrophobic and hydrophilic colloidal particles on these shape transformations. We find that these shape transformations persist even at high interfacial colloidal densities, despite the colloids disrupting the molecular interfacial crystal's topology. We employ computer simulations to elucidate the role of colloidal particles in droplet shape control of these widely employed emulsions. Surprisingly, we observe that the particles serve as incompressible inclusions, which do not disrupt the out-of-plane buckling of the interfacial crystal. Our findings demonstrate temperature-control of droplet shape transformations and self-division in emulsions costabilized by colloidal particles and molecular surfactants. The fundamental mechanisms uncovered here may have broad implications for biological systems, enable unexplored strategies for microcargo delivery and release, and inspire unconventional approaches in smart material design.