An apparatus and method are provided for the two-stage selective oxidation of carbon monoxide to carbon dioxide in a fuel stream comprising hydrogen and carbon monoxide. The apparatus includes primary and secondary reaction chambers, which deliver a hydrogen-rich outlet gas stream having a carbon monoxide concentration of less than about 5 ppm. When an increase in the carbon monoxide concentration in the outlet stream of the primary reaction chamber is detected, then the flow through the primary reaction chamber is reversed. The selective oxidizer employs a temperature-based control strategy as an oxygen-containing gas stream flow rate adjustment around the flow rate initially set in direct proportion to the fuel gas stream flow rate. The control strategy regulates the amount of oxygen-containing gas mixed with the gaseous fuel stream as a function of the difference between the temperature at a location at or near the end of the primary reaction chamber and the temperature at the outlet of the primary reaction chamber.