Can an adverse density difference across a surface be stabilized by heating from above?

We investigate the possibility of stabilizing a Rayleigh-Taylor experiment by imposing a small upward temperature gradient. We find that if the two fluids have equal thermal conductivities nothing can be accomplished. If either thermal conductivity is much greater than the other, the small gradient is always stabilizing. If the thermal conductivities are of the same order of magnitude the small gradient can be stabilizing or destabilizing depending on the thermal expansion coefficients. We have used a Darcy model so that we can derive formulas and present a physical explanation of what we find.