This contribution presents a coupled thermo-viscoelastic formulation for the analysis of complex geometrically exact beam systems, particularly suited for modeling morphing devices made of Shape Memory Polymers (SMPs). The method permits capturing the thermo-mechanical interaction by simultaneously solving thermodynamic and quasi-static mechanical equations. Viscoelasticity is modeled through the Generalized Maxwell model, endowed with temperature-dependent relaxation properties following the Time-temperature Superposition Principle (TTSP) [1]. This temperature-dependent rheological model allows for an accurate and efficient reproduction of the Shape Memory Effect [2]. The rate-dependent viscoelastic constitutive equations are directly applied to the beam strain and stress measures. By employing the trapezoidal rule for the time integration of the evolution laws, this one-dimensional approach ensures high computational efficiency as no additional unknowns, beyond those of a rate-independent elastic material, are required [3]. High efficiency is also pursued by discretizing the governing equations with isogeometric collocation (IGA-C), a method that bypasses the need for element integration while keeping the key IGA attributes, such as high-order accuracy and advanced geometric capabilities [4]. The proposed method is compared with results stemming from a three-dimensional model, demonstrating its capability to predict the complex thermo-mechanical response of SMP beam systems. These results highlight the potential of the proposed approach for the design of 4D-printed programmable objects, with particular relevance, for example, to personalized biomedical devices. REFERENCES [1] J. D. Ferry, Viscoelastic properties of polymers, Third Edition, New York, John Wiley & Sons, 1980. [2] G. Ferri and E. Marino, Simulating morphing of shape memory polymer beam systems with complex geometry and topology, J Mech Phys Solids, vol. 203, p. 106215, 2025. [3] G. Ferri, D. Ignesti, and E. Marino, An efficient displacement-based isogeometric formulation for geometrically exact viscoelastic beams, Comput Methods Appl Mech Eng, vol. 417, p. 116413, 2023. [4] F. Auricchio, L. B. da Veiga, T. J. R. Hughes, A. Reali, and G. Sangalli, Isogeometric collocation methods, Mathematical Models and Methods in Applied Sciences, vol. 20, no. 11, pp. 2075–2107, 2010.