<p>Thermal error is the primary factor affecting the accuracy of gear grinding machines. To improve gear grinding accuracy, it is critical to determine the effect of thermal errors on gear tooth surface errors and identify the pivotal thermal errors. In the paper, a pivotal thermal error identification method combining the thermal error-tooth surface error model and improved Sobol sensitivity analysis is proposed. Firstly, the worm wheel tooth surface model is established using the conjugate surface envelope theory, and the thermal error-tooth surface error model is constructed based on the principle of conjugate grinding. Then, the improved Sobol method is applied to quantify the error sensitivity under different temperature states, thereby identifying the pivotal thermal errors that affect the gear tooth surface accuracy. Finally, thermal error measurement experiments are conducted under various working conditions to determine the variation ranges of different thermal errors. The validity of these results is verified through numerical modification and simulation analysis of the pivotal thermal errors. The results demonstrate that compensating for pivotal thermal errors reduces the maximum, average, and root mean square values of the gear tooth surface error by over 70%, confirming the accuracy of the identification method.</p>