A cooling system (10) is provided for use with a fuel processing subsystem (12) for reducing a level of carbon monoxide in a reformate flow (14) for a proton exchange membrane fuel cell system (16). The fuel processing subsystem (12) includes first and second preferential oxidizers (18, 20) to oxidize the carbon monoxide carried in the reformate flow. The reformate cooling system (10) includes a coolant flow path (30), a reformate flow path (32), and first, second, third, and fourth heat exchanger core portions (34, 36, 38, 40). The core portions (36 40) are arranged in numbered sequence along the reformate flow path (32) with the first and second core portions (34, 36) located upstream of the first preferential oxidizer (18), and the third and fourth core portions (38, 40) located downstream of the first preferential oxidizer (18) and upstream of the second preferential oxidizer (20). The first and second core portions (34, 36) are arranged in numbered sequence along the coolant flow path (30), one of the third and fourth core portions (38, 40) is arranged upstream of the first core portion (34) along the coolant flow path (30), and the other of the third and fourth core portions (38, 40) is arranged downstream of the second core portion along the coolant flow path (30).