For application to planetary ionospheres we have derived diffusion and heat flow equations for a fully ionized three-component plasma and for a partially ionized three-component plasma using a formulation that is valid for arbitrarily large temperature differences between the interacting species. These equations can be applied to ionospheric situations where steady state, collision-dominated conditions prevail and where the species drift velocities are much less than the species thermal speeds (low Mach numbers). The application of the diffusion and heat flow equations to the F region and topside terrestrial ionosphere indiates that the various transport coefficients can exhibit significant variation with the different species temperature ratios.