Heat conduction properties are investigated in a molecular junction modeled as a two-strand ladder with strongly asymmetric thermal transport pathways. By confining anharmonic contributions to only one of the strands, it is shown that tuning of the interstrand coupling can lead to normal heat transport and to the emergence of a well-defined temperature gradient. More interestingly, thermal rectification is obtained around a critical value of the interstrand interaction and by appropriate asymmetries induced by the coupling to the thermal baths.