Mathematical models of an Intermediate Temperature Solid Oxide Fuel Cell (IT-SOFC) with indirect internal reforming operation (IIR-SOFC) fueled by methane were developed. The models were based on a steady-state heterogeneous two-dimensional tubular-design SOFC. The benefit in adding oxygen to methane and steam as the feed for autothermal reforming reaction on the thermal behavior and SOFC performance was simulated. The results indicated that smoother temperature gradient with lower local cooling at the entrance of the reformer channel can be achieved by adding a small amount of oxygen. However, the electrical efficiency noticeably decreased when too high oxygen content was added due to the loss of hydrogen generation from the oxidation reaction; hence, the inlet oxygen to carbon (O/C) molar ratio must be carefully controlled. Another benefit of adding oxygen is the reduction of excess steam requirement, which could reduce the quantity of heat required to generate the steam and eventually increases the overall system performance. It was also found that the operating temperature strongly affects the electrical efficiency achievement and temperature distribution along the SOFC system. By increasing the operating temperature, the system efficiency increases but a significant temperature gradient is also detected. The system with a counter-flow pattern was compared to that with a co-flow pattern. The co-flow pattern provided smoother temperature gradient along the system due to better matching between the heat supplied from the electrochemical reaction and the heat required for the steam reforming reaction. However, the electrical efficiency of the co-flow pattern is lower due to the higher cell polarization at a lower system temperature. (C) 2010 Professor T. Nejat Veziroglu. Published by Elsevier Ltd. All rights reserved.