Composite propellants are commonly used in the fabrication of solid rocket motors (SRMs) for space vehicles. A key factor affecting motor safety is structural damage in the propellant due to abnormal heating during storage or service. Thus, a comprehensive investigation into the ignition and combustion behavior of composite propellants under heated conditions is imperative. To investigate the thermal safety performance of SRMs in high-temperature environments, a three-dimensional cook-off numerical model was developed for a small SRM with ammonium perchlorate (AP)/hydroxyl‑terminated polybutadiene (HTPB) propellant. The model simulates thermal decomposition and combustion at ambient temperatures of 600 K, 800 K, and 1000 K, obtaining cook-off response characteristics and pressure load responses on the casing structure. The model mathematically describes and simulates the entire cook-off process of the solid rocket motor. Results show ignition at the propellant bottom edge under three cook-off conditions, with significant fast cook-off characteristics. The ignition delay times are 113.5 s at 1000 K, 232.2 s at 800 K and 852.6 s at 600 K, decreasing with increasing ambient temperature. Changes in ambient temperature have no significant effect on the ignition temperature of the propellant. Numerical calculations of shell response were performed for the cook-off condition at an ambient temperature of 800 K. The casing ruptures at the ignition site, causing the nozzle to separate from the main body, which remains relatively intact. The motor body develops longitudinal cracks and splinters, with cracks propagating towards the ends. The maximum propellant pressure reached nearly 700 MPa when the case responded.