This study examines the thermodynamic and numerical analyses of a methane-fed solid oxide fuel cell (SOFC) over a temperature range varying between 873 K and 1273 K. These analyses were conducted to investigate and compare the performance of the SOFC under various operating conditions in detail. As part of the thermodynamic analysis, important parameters such as cell voltage, power density, exergy destruction, entropy generation, thermal efficiency, and exergy efficiency were calculated. These calculations were used to conduct energy and exergy analyses of the cell. According to the findings, an increase in operating temperature led to a significant improvement in performance. At the initial conditions where the SOFC operated at a temperature of 1073 K and a current density of 9000 A/m2, it was observed that when the temperature increased by 200 K while keeping the current density constant, the power density increased by a factor of 1.90 compared to the initial state, and the thermal efficiency increased by a factor of 1.45. Under a constant current density, the voltage and power density values were 1.0081 V, 1.0543 V, 2337.13 W/m2, and 2554.72 W/m2 at operating temperatures of 1073 K and 1273 K, respectively. Under a current density of 4500 A/m2, the entropy generation in the cell was determined to be 29.48 kW/K at 973 K and 23.68 kW/K at 1173 K operating temperatures. The maximum exergy efficiency of the SOFC was calculated to be 41.67% at a working temperature of 1273 K and a current density of 1500 A/m2. This study is anticipated to be highly significant, as it examines the impact of temperature variation on exergy analysis in SOFC, validating both numerical and theoretical results, thus providing a crucial roadmap for determining optimized operating conditions.