The Lagrange test was conducted to investigate the shock ignition and growth of HMX-based polymer bonded explosives (PBXs) under different temperature conditions. In this study, three temperature conditions, 25 °C, 80 °C and 120 °C were used. The pressure history values along the direction of the detonation wave propagation were obtained and presented as the characteristics of the shock ignition and growth. Manganin piezoresistive pressure gauges were used to measure the pressure. The results showed that the distance to detonation was clearly reduced as the temperature was increased. A distance greater than 9 mm at 25 °C was changed to less than 3 mm at 120 °C. In order to understand this phenomenon in more detail, the Lee-Tarver ignition and growth model was employed to simulate the Lagrange test, and the simulated pressures were compared with the measured pressures. The results demonstrated that the intrinsic mechanism of the phenomenon was that the high temperature changed both the equation of state of the unreacted explosive and the chemical reaction rate. It was remarkable that the parameter R2 in the model was reduced from −0.05835 to −0.06338, and the parameter G1 in the model was increased from 1.3 to 2.12.