Consideration is given to a system consisting of two parallel vertical channels that share a common wall across which heat is transferred from one channel to the other. The other walls of the system are characterized by prescribed surface temperatures that exceed the ambient temperature, and this induces a buoyancy-driven upflow in the channels. To cope with the strong interaction between the channels, a solution scheme was employed in which each channel was visited successively and iteratively. The single-channel solutions that were performed at each visitation were also iterative in character, with the computations carried out with a parabolic finite-difference method. Three parameters were varied during the course of the computations. These Included the dimensionless channel height, a dimensionless temperature difference, and the dimensionless position of the common wall between the channels. Results are presented for the surface-integrated heat transfer at each channel wall, the total system heat transfer, and the convective energy efflux from the respective channels. Local heat flux distributions are also presented, as are the distributions of the temperature along the common wall.