Fuel cells are a promising source of clean energy. To find optimal parameters for their operation, modeling is necessary, which is quite difficult to implement taking into account all the significant effects occurring in them. We aim to develop a previously unrealized model in COMSOL Multiphysics that, on one hand, will consider the influence of electrochemical heating and non-isothermal fluid flow on the temperature field and reaction rates, and on the other hand, will demonstrate the operating mode of the Solid Oxide Fuel Cell (SOFC) on carbonaceous fuel. This model incorporates a range of physical phenomena, including electron and ion transport, gas species diffusion, electrochemical reactions, and heat transfer, to simulate the performance of the SOFC. The findings provide a detailed view of reactant concentration, temperature, and current distribution, enabling the calculation of power output. The developed model was compared with a 1-kW industrial prototype operating on hydrogen and showed good agreement in the volt-ampere characteristic with a deviation not exceeding 5% for the majority of the operating range. The fuel cell exhibits enhanced performance on hydrogen, generating 1340 W/m2 with a current density of 0.25 A/cm2. When fueled by methane, it produces 1200 W/m2 at the same current density. Using synthesis gas, it reaches its peak power of 1340 W/m2 at a current density of 0.3 A/cm2.