A thermal analysis of the anode, cathode and electrolyte of a practical solid oxide fuel cell (SOFC) is performed. Electrochemical impedance spectroscopy with two-electrode set-up is employed on an anode-supported microtubular SOFC. This cell is an intermediate temperature SOFC composed of a Ni/(ZrO2)0.9(Y2O3)0.1, cermet anode, a La0.8Sr0.2Ga0.8Mg 0.2O2.8, electrolyte, and an (La0.6Sr 0.4)(Co0.2Fe0.8)O3 cathode. A common equivalent circuit is applied to impedance spectra to acquire the resistances at the anode and cathode, and the cell Ohmic resistance. By numerically integrating these resistances, overpotentials are evaluated. The overpotentials and entropy balances, i.e., the single electrode Peltier heats, at the anode and cathode give individual heat production rates. By analytically integrating energy balance equations incorporating the heat production rates, temperatures at the anode and cathode surfaces are obtained and agree well with those measured with thermocouples.