This contribution presents a novel computational approach for the programming and morphing of geometrically exact beam systems made of Shape Memory Polymers (SMPs). To properly model the thermo-viscoelastic problem, we integrate the viscoelastic Generalized Maxwell model with the Time-Temperature Superposition Principle (TTSP), enabling an accurate prediction of material relaxation properties as a function of temperature [1]. The temperature-dependent rheological model is directly applied to the one-dimensional beam strain and stress measures, without introducing additional unknowns beyond those of a rate-independent elastic formulation [2]. High-order spatial accuracy and exact geometry representation are ensured through the isogeometric collocation (IGA-C) method. Time evolution is captured using the trapezoidal rule, allowing for a stable and second-order-accurate time integration of rate-dependent variables. Furthermore, the formulation incorporates transient heat conduction, convection, and temperature dependent boundary conditions, and it is capable to support arbitrarily curved initial geometries. This key features makes this computational approach particularly suited for the analysis of 4D printed biomedical devices, such as patient-tailored cardiovascular stents. Numerical applications confirm the effectiveness of the formulation in predicting shape programming and recovery in SMP-based biomedical devices. The results underscore its potential for advancing the design of next-generation 4D printed patient-tailored cardiovascular stents.