In this work we investigate heat conduction along a ladder-model conformed by two coupled one dimensional lattices with different anharmonicity. We study how the interchain coupling modifies the thermal properties of the isolated systems. For a large enough coupling strength, we demonstrate that a harmonic lattice interacting with an anharmonic one is able to support a linear thermal gradient when it is connected to two heat reservoirs at different temperatures. We estimate this critical coupling by applying the self-consistent phonon theory (SCPT) to the anharmonic counterpart. By exchanging the heat baths connections between the harmonic and the anharmonic chains, our results show that the coupled system reveals as a thermal rectifier.