The large-vortex model is used to derive relationships for turbulent transport properties, flow velocity and temperature profiles, and for heat transfer, given arbitrary values of the Reynolds and Prandtl numbers of the heat-transfer agent. The inclusion of special features of the turbulent flow structure and of the processes of momentum and heat transfer helps refine the relationships of the hydrodynamic analogy of heat- and mass transfer as applied to flows of different (with respect to the Prandtl number) heat-transfer agents.