High temperature Solid Oxide Fuel Cells (SOFCs) represent a promising and efficient technology for electrochemical conversion of chemical energy of a fuel into electrical energy. The future development of such technology depends on the availability of detailed and efficient multi-dimensional modeling tools. In this paper, a new three-dimensional finite element algorithm, based on a detailed mathematical model for fuel cells and on the fully explicit Artificial Compressibility (AC) Characteristic Based Split (CBS) scheme, is employed for the effective and efficient modeling of heat and mass transport phenomena coupled with electrochemical reactions in SOFC. The thermal field in the fuel cell is analyzed and the influence of the operating temperature on the fuel cell overall performance is investigated. The three-dimensional results obtained in this work are also compared to the results carried out by employing the two-dimensional version of the present scheme. The results are validated against experimental data available in the literature.