Quartz flexible accelerometer (QFA) has been widely applied in the inertial navigation system (INS) due to its high accuracy and reliability. However, the performance of QFA is susceptible to the ambient temperature. Considering the thermal capacity and temperature hysteresis behavior of the magnetic components in QFA, the drift in the output signal of QFA along with the ambient temperature is not only related to the current temperature, but also affected by the spatiotemporal gradient field of temperature. To address this issue, a temperature compensation model for the output signal of QFA based on the gated recurrent unit (GRU) is proposed in this paper. The model parameters of GRU are trained by the separated scale factor and zero bias of QFA measured by the discrete calibration method in the high-precision temperature box. Leveraging the great nonlinear curve fitting and memory capabilities of GRU, the temperature compensation model could effectively predict and compensate for the temperature drift portions on basis of the spatiotemporal gradient information of temperature. Two sets of temperature cycling experiments are conducted under the same conditions, one for training the model and the other for testing the compensation effect of the model. Experiment results show that the residual error of QFA scale factor after compensation is better than 10ppm and the root mean square error (RMSE) is better than 3ppm, the residual error of zero bias is better than 7ug and the RMSE is better than 4ug. Compared to uncompensated QFA, the RMSEs of compensated scale factor and zero bias are improved by about 100 times. The proposed temperature compensation model significantly improves the temperature stability of QFA, which would enhance the navigation accuracy of INS effectively.