Shape memory polymers (SMPs) are advanced materials capable of recovering their original configuration in response to external stimuli such as heat, light, and electric or magnetic fields. These properties demonstrate their potential in applications like deployable morphing structures in aerospace, vessel embolization, and flexible tools for minimally invasive surgical procedures in medicine. SMPs exhibit complex behaviors, including shape recovery, stress relaxation, and phase transitions (e.g., from rubbery to glassy states), which are challenging to capture through experimental methods alone. Numerical models provide an effective means to analyze these behaviors under various multiphysics conditions, facilitating the systematic exploration of material properties to optimize performance across applications. However, existing models typically focus on behavior before the crystalline phase, leaving a gap in understanding its performance in the crystalline phase, where thermo-mechanical properties may change at temperatures lower than those in the glassy state. In this study, we investigate SMP response over a broad temperature range and propose a new phenomenological three-phase model that accounts for interactions among the rubbery, glassy, and crystalline phases under one-dimensional uniaxial loading conditions. Isothermal tests examine the stress-strain behavior at fixed temperatures, while thermo-mechanical tests are used to investigate phase transitions. The numerical model, developed from experimental data, demonstrates the potential to accurately predict SMP behavior across a wide temperature range. This study lays the groundwork for applying the proposed model to multi-phase systems, enabling the prediction of SMP behavior under varying thermo-mechanical conditions.