The conjugate heat transfer across a thin horizontal wall separating two fluid-saturated porous media at different temperatures is investigated numerically and asymptotically. The solution for large Rayleigh numbers is shown to depend on two nondimensional parameters : alpha, the ratio of the thermal resistance of the boundary layer in the hot medium to the thermal resistance of the wall, and beta, the ratio of the thermal resistances of the boundary layers in the two media. The overall Nusselt number is an increasing function of a tending to zero for alpha --> 0, and to a finite maximum value for alpha --> infinity.