The traditional temperature stress detection method is restricted by the detection principle and the efficiency of sensor elements, so it is difficult to monitor the temperature stress of continuously welded rail (CWR) quickly and accurately in real time. Based on the principle of acoustic elasticity, the optimal incident angle of ultrasonic longitudinal wave is calculated by using Snell theorem, and the real-time temperature stress detection of CWR is realized through the neutral temperature point. The hardware and software systems of temperature stress on-line monitoring are built up to practice the theoretical algorithm. The real-time monitoring waveform is sent to the cloud server by mobile network transmission. The peak of the original waveform is taken as the characteristic data, and the interference of residual stress on the temperature stress detection results is removed by calibration experiment. The results show that the critical refracted longitudinal wave can effectively measure the temperature stress of CWR rail. Combined with the established hardware and software system, it provides a new way for the management of key parameters of CWR service performance. It is suggested that the proposed rail temperature stress monitoring scheme be popularized.