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In this article, to heighten the accuracy of thermal error forecast model of motorized spindle, a thermal error modeling method of kernel extreme learning machine based on snake optimization is advanced. ANSYS simulation software is used to simulate the thermal characteristics of the electric spindle, and the temperature field distribution is acquired. Then, according to the experimental requirements, a platform is built to obtain the axial temperature and thermal displacement data of the spindle. The FCM algorithm and grey relation analysis are utilized to optimize the survey points, and ten measuring points are reduced to four. The SO-KELM model is established based on the snake-optimized kernel extreme learning machine. Comparing the established model with the KELM model and PSO-KELM model, it is proved that SO-KELM model has good prediction accuracy and stability.