This paper investigates the mechanism of thermal-induced errors in interferometric fiber optic gyroscopes (IFOGs) caused by temperature changes in a vacuum environment, proposing a method for calculating thermal-induced errors in small fiber coils. Firstly, based on the Shupe effect and the thermal stress caused by temperature changes around the fiber coil, a three-dimensional thermal-induced error model for small fiber coils is established. Secondly, a spatial fiber optic inertial measurement unit (IMU) model is designed using the Creo 3D modeling software (creo 7.0.0). The model is then imported into the Ansys finite element simulation software (ANSYS Workbench 15.0), where a temperature field is applied to the IMU based on actual temperature profiles to obtain the temperature distribution of the fiber coil at different times in a vacuum state. These data are then used in the three-dimensional thermal-induced error model to calculate the thermal-induced error of the FOG. Finally, a thermal vacuum experimental platform is set up to collect temperature variation data from the inertial measurement components. The experimental data are compared with the three-dimensional error model proposed in this paper as well as traditional error models. The root mean square error is approximately 33% lower than that of traditional error calculation methods, which also proves the theoretical accuracy.