Hydroxyl-terminated polybutadiene (HTPB) is frequently employed as a key component of propellant binder in missiles or solid rockets. Understanding its shock response can help us to deepen our understanding of the shock response in its composites. Considering that missiles or solid rockets often need to operate in various temperature environments, investigating the shock wave propagation within the HTPB and its spallation behaviors under different temperatures and impact velocities is critical for understanding its failure modes. By employing large-scale molecular dynamics simulations, we provide a thorough analysis of the shock propagation and spallation strength of the HTPB under different initial temperatures and impact velocities. The quantification of the spallation strength is done by indirect methods based on the acoustic and modified acoustic assumptions and by the direct method that analyzes atomic stress in the spallation region. Our simulation results reveal that the spallation strength is associated with the impact velocity acting on the materials as well as the initial temperature. When the initial temperature is below the glass transition temperature, the spallation strength exhibits a monotonic decrease with increasing impact velocity. In contrast, such monotonicity is not observed above the glass transition temperature. Our findings furnish insights at the molecular level regarding the spallation processes in HTPB under varying impact loadings and temperature conditions, thereby facilitating the design of HTPB materials with enhanced resistance to impact loading.