Compared with the traditional gyros, Fiber optic gyroscope (FOG) based on sagnac effect has the significant features, such as, long life, low cost, wide dynamic range, etc. These features have developed new applications of the gyroscope not only in industrial application area but also in aerospace application area. Now, the FOG has played a very important role in shipborne Strapdown Inertial Navigation System (SINS). The fiber coil, as one of the most critical components in FOG, is extremely sensitive to changes in temperature. Here, by study the environment temperature in shipborne SINS, the temperature performance of the FOG was analyzed. Firstly, on the base of the research about the theory of Shupe non-reciprocal errors caused by temperature, the discrete mathematics formula of the temperature error in FOG of SINS was built .Then the element model of the fiber coil in SINS was built based on the discrete model of the fiber coil in temperature error in FOG. A turn-by-turn quantization temperature bias error model is establish. Finally, based on the temperature models mentioned above, the temperature performance of FOG in shipborne SINS was analyzed. With finite element analysis, numerical simulations were carried out to quantitatively analyze the angular error induced by temperature excitation in SINS. The model was validated by comparing numerical and experimental results.