The performance and the operation viability of solid oxide fuel cells (SOFC) fueled by reformed methane using the concept of non-uniform potential operation were evaluated by one-dimensional finite difference analysis. Two thermal constraints including maximum acceptable stack temperature gradient and maximum stack temperature were the criteria for considering the operation viability. The average power density was used as a performance indicator. In addition, two major process parameters: fuel and air inlet temperatures and the operating voltage were examined to determine the suitable values for different viabilities. The results revealed that non-uniform potential SOFC with two stack sections operating at different voltages could not offer a significantly higher average power density compared with the uniform potential SOFC owing to thermal constraint limitations. The installation of coolers between the stacks is important and it could offer 12.8% improvement in average power density.