If Soret number > 0 : An increase in T will cause not only a decrease in the density, but also a decrease in the mass fraction of solute C that will generate even a decrease in density. This is called thermal gradients and cooperative solutal; the solute (term for, remember, the heaviest of the two components of the binary mixture) migrates to cold regions.
All I know about the Dufour effect is that the energy flux caused by a composition gradient is termed the Dufour or diffusion-thermo effect. It is the reciprocal phenomenon to the Soret effect.