Origami robots are becoming very popular due to their excellent morphing abilities and ease of manufacturing. The use of Shape Memory Materials (SMM) for actuation in such structures have not only been proven to make them robust and adaptable to different conditions but also to provide special capabilities. Particularly, Shape Memory Alloy (SMA) actuators have been used for the self-folding/deployment of smart structures. This study presents a Finite Element Analysis (FEA) based thermomechanical model which couples a torsional SMA actuator with a rigid host structure using Shape Memory Polymer (SMP). A specific technique is used for the solution convergence of a complex nonlinear model. After folding the structure to an initial rotation, the influence of SMP stiffness on a Shape Memory Effect (SME) activated rotational motion is investigated. Additionally, the influence of SMP on the global rotational stiffness of such inherently soft structures is studied. The model serves as a starting point for a FEA-based design approach of SMM-equipped singular origami structures and can be topologically optimized for specific applications.