Creation of an autothermal system by coupling an endothermic to an exothermic reaction demands the matching of the thermal requirements of the two reactions. The application under study is a solid oxide fuel cell (SOFC) with indirect internal reforming (IIR) of methane, whereby the endothermic steam reforming reaction is thermally coupled to the exothermic oxidation reactions. A steady-state model of an IIR-SOFC has been developed to study the mismatch between the thermal load associated with the rate of steam reforming at typical SOFC temperatures and the local amount of heat available from the fuel cell reactions. Results have shown a local cooling effect, undesirable for ceramic fuel cells, close to the reformer entrance. The system behaviour towards changes in catalyst activity, fuel inlet temperature, current density, and operating pressure has been studied. Increasing the operating pressure is shown to be an effective way of reducing both the local cooling caused by the reforming reactions and the overall temperature increase across the cell. Simulations for both counter-flow and co-flow configurations have been performed and compared.