A steam-hydrocarbon reforming process comprising: (a) introducing a reformate into a first inlet of a reactor, the reactor containing a reforming catalyst, the reformate having a first inlet temperature ranging from 550°C to 725°C, reacting the reformate in the presence of the reforming catalyst under reaction conditions sufficient to form additional hydrogen in the reformate, and withdrawing the reformate with additional hydrogen from a first outlet of the reactor at a first outlet temperature ranging from 575°C to 725°C; (b) introducing a reformed gas into a second inlet of the reactor at a second inlet temperature ranging from 800°C to 975°C, passing the reformed gas co-currently to the reformate in the reactor, transferring heat from the reformed gas to the reformate in the reactor, and withdrawing the reformed gas from a second outlet of the reactor at a second outlet temperature ranging from 675°C to 925°C; (c) introducing a reformer feed gas comprising at least a portion of the reformate from the first outlet of the reactor into a plurality of reformer tubes of a reformer, the plurality of reformer tubes containing a second reforming catalyst, reacting the reformer feed gas comprising at least a portion of the reformate in the presence of the second reforming catalyst under reaction conditions sufficient to form the reformed gas containing hydrogen, and withdrawing the reformed gas from the plurality of reformer tubes; and (d) introducing an oxidant gas mixture containing oxygen and a fuel into a combustion section of said reformer, combusting the fuel and the oxygen to form combustion product gases and generate heat to supply energy for reacting the reformate in the plurality of reformer tubes, and withdrawing the combustion product gases from the combustion section; wherein the reactor is provided with a heat transfer surface area, the heat transfer surface area for exchanging heat indirectly between the reformate and the reformed gas during the reacting of the reformate in the reactor wherein the heat transfer surface area is effective to decrease the temperature of the reformed gas from the second inlet temperature ranging from 800°C to 975°C to the second outlet temperature ranging from 675°C to 925°C and to maintain the first outlet temperature of the reformate between 575°C and 725°C; and wherein no sulfur compounds are removed from the reformed gas after withdrawing the reformed gas from the second outlet of the reactor. (a) introducing a reformate into a first inlet of a reactor, the reactor containing a reforming catalyst, the reformate having a first inlet temperature ranging from 550°C to 725°C, reacting the reformate in the presence of the reforming catalyst under reaction conditions sufficient to form additional hydrogen in the reformate, and withdrawing the reformate with additional hydrogen from a first outlet of the reactor at a first outlet temperature ranging from 575°C to 725°C; (b) introducing a reformed gas into a second inlet of the reactor at a second inlet temperature ranging from 800°C to 975°C, passing the reformed gas co-currently to the reformate in the reactor, transferring heat from the reformed gas to the reformate in the reactor, and withdrawing the reformed gas from a second outlet of the reactor at a second outlet temperature ranging from 675°C to 925°C; (c) introducing a reformer feed gas comprising at least a portion of the reformate from the first outlet of the reactor into a plurality of reformer tubes of a reformer, the plurality of reformer tubes containing a second reforming catalyst, reacting the reformer feed gas comprising at least a portion of the reformate in the presence of the second reforming catalyst under reaction conditions sufficient to form the reformed gas containing hydrogen, and withdrawing the reformed gas from the plurality of reformer tubes; and (d) introducing an oxidant gas mixture containing oxygen and a fuel into a combustion section of said reformer, combusting the fuel and the oxygen to form combustion product gases and generate heat to supply energy for reacting the reformate in the plurality of reformer tubes, and withdrawing the combustion product gases from the combustion section;