Abstract: The present invention is a method and apparatus (vessel) for providing a heat transfer rate from a reaction chamber through a wall to a heat transfer chamber substantially matching a local heat transfer rate of a catalytic thermal chemical reaction. The key to the invention is a thermal distance defined on a cross sectional plane through the vessel inclusive of a heat transfer chamber, reaction chamber and a wall between the chambers. The cross sectional plane is perpendicular to a bulk flow direction of the reactant stream, and the thermal distance is a distance between a coolest position and a hottest position on the cross sectional plane. The thermal distance is of a length wherein the heat transfer rate from the reaction chamber to the heat transfer chamber substantially matches the local heat transfer rate.