As a high-precision angular sensor, the interferometric fiber-optic gyroscope (FOG) usually shows high sensitivity to disturbances of the environmental temperature. To research the related influencing factors of influencing the thermal-induced rate error of an FOG is essential to enhance precision and environmental suitability. This paper starts with the factors neglected in past research to derive the thermal-induced error model of a fiber coil including various factors of equivalent radius, asymmetry of fiber tail, cross-layer leap, and so on in detail, and then translates this error into the inner product form of penalty factor matrix and temperature field matrix. Then, the mathematical model and the three-dimensional temperature field model of the fiber coil with the quadrupolar winding pattern is built, which includes the optic core, coating, glue, packing paper, and accurate temperature boundary conditions. The penalty factor matrix and temperature field matrix can be obtained from these models. Finally, the advancement of this revised the thermal-induced rate error model has been verified through simulation and experimental comparison.