Thermal control is an important aspect of spacecraft design, particularly in the case of crewed vehicles, which must maintain a precise internal temperature at all times in spite of sometimes drastic variations in the external thermal environment and internal heat loads. The successes of the Apollo, Space Shuttle, and International Space Station programs have shown that this can be accomplished for short-term missions to the Moon and long-term missions to Low Earth Orbit (LEO); however, crewed spacecraft traveling beyond LEO are expected to encounter more challenging thermal conditions with significant variations in both the heat rejection requirements and environment temperature. Such missions will require radiator systems with high turndown ratios, defined as the ratio between the maximum and minimum heat rejection rates achievable by the radiator system. Current radiators are only able to achieve turndown ratios of 3:1, far less than the 12:1 turndown ratio which is expected to be required on future missions. An innovative radiator concept, known as a morphing radiator, uses the temperature-induced shape change of shape memory alloy (SMA) materials to achieve a turndown ratio of at least 12:1. Predicting the behavior of morphing radiators requires analysis tools that are capable of accurately representing the driving physics. However, developing mathematical and computational models of morphing radiators is challenging due to the presence of a unique type of two-way thermomechanical coupling. This coupling is not present in traditional, fixed-geometry radiators and has not been widely considered in the literature. Furthermore, although many existing simulation tools are capable of analyzing certain types of thermomechanically coupled problems, general problems involving radiation and deformation cannot be modeled natively in these tools. This work presents an analysis framework which has been developed to overcome these present shortcomings. Several example problems are used to demonstrate the ability of the framework to simulate realistic problems involving morphing radiators. In addition, a prototype morphing radiator was designed, fabricated, and subsequently tested in a thermal environment similar to one in which the radiator is expected to operate on a future mission. Following the experimental study, a detailed finite element model of the prototype was developed and executed using the framework. In spite of some discrepancies resulting from shortcomings in the SMA constitutive model, the model predictions generally agree with the experimental data, giving confidence that the framework is able to accurately represent the thermomechanical coupling present in morphing radiators.