Demodulation methods play a critical role in achieving high-performance interferometric fiber-optic temperature sensors. However, the conventional passive 3 × 3 coupler demodulation method overlooks certain issues, such as the non-1:1:1 splitting ratio of the coupler, resulting in a non-ideal phase difference in the three output interference signals. These problems significantly impact the measurement results of interferometric temperature sensors. In this paper, we propose a novel arc-tangent method based on a 3 × 3 coupler and a demodulation algorithm combining long short-term memory (LSTM) with an artificial bee colony (ABC). The arc-tangent method is employed to enhance the input phase signal of the ABC-LSTM network model and establish a nonlinear mapping between the phase signal and temperature, effectively preventing the influence of the spectral ratio and phase difference of the 3 × 3 coupler on temperature demodulation. The proposed ABC-LSTM method achieves high-resolution measurements with an interval of 0.10 °C, and the absolute error is below 0.0040 °C within the temperature range of 25.00–25.50 °C. To demonstrate the stability and adaptability of the proposed method under long-term constant temperature conditions, we conducted measurements for approximately three hours in a controlled temperature environment set at 25.00 °C. Experimental results indicate that the maximum error of LSTM-ABC method remains around 0.0040 °C, outperforming the conventional algorithm (0.0095 °C). Furthermore, when comparing the average error values of the conventional passive 3 × 3 coupler method (0.0023 °C), LSTM model (0.0019 °C), and ABC-LSTM model (0.0014 °C), it is evident that the demodulation results of the ABC-LSTM method exhibit the highest level of stability. Therefore, the ABC-LSTM method enhances the accuracy and reliability of interferometric fiber-optic temperature-sensing systems.