When the solid rocket motor is in storage and the air conditoning fails, it is necessary to analyze the effect of the temperature gradient on the performance of the motor and the integrity of the propellant grain under the condition of long time high temperature and low temperature storage. Based on the thermoviscoelastic constitutive model and finite element numerical simulation, heat conduction and thermodynamic coupling analysis were carried out. The temperature field distribution of the grain was given. The envelop of internal ballistic performance of the motor was calculated by combining the zero dimensional internal ballistic control equations. And the relationships between equvialent stress and equvialent strain of grain, insulation-grain interface and insulation-shell interface with time were given. The analysis results indicate that during the temperature cycling process, the temperature gradient has minimal impact on the internal ballistics. Additionally, the maximum equivalent stress/strain of the propellant grain and both interfaces remain below the relevant technical test criteria, ensuring no damage to the motor propellant grain or interfaces.