The present invention is a natural gas steam reforming method for generating an output gas mixture of carbon dioxide and hydrogen, including the following steps. (1) Combusting a portion of the natural gas with an oxidizing agent to generate heat, superheated steam, and a gas mixture of carbon dioxide, carbon monoxide, and hydrogen. (2) Steam reforming the gas mixture with additional superheated steam under steam-rich conditions to transform a remaining portion of the natural gas into carbon dioxide, carbon monoxide, and hydrogen. (3) Water-gas-shifting any residual carbon monoxide into additional carbon dioxide and additional hydrogen by utilizing a water-gas-shift catalyst downstream of the steam reforming step, thereby producing an effluent gas mixture that is predominantly carbon dioxide and hydrogen. (4) Boiling water in a top-to-bottom linear countercurrent heat exchanger to generate the superheated steam by transferring heat released in the water-gas-shifting step, where as the water is gravitationally and thermally stratified from top to bottom with a top portion boiling into steam, the steam continues to rise and is additionally heated in the top-to-bottom linear countercurrent heat exchanger. (5) And, utilizing the superheated steam produced as a reactant in the steam reforming step and the water-gas-shifting step to assist in reformation of the natural gas into carbon dioxide and hydrogen.