We propose an innovative formulation for the coupled thermo-mechanical analysis of geometrically exact beams and beam systems made of shape memory polymers (SMPs). The formulation couples the thermal and mechanical problems, including transient heat conduction, convection, and temperature-dependent boundary conditions. The shape memory effect is reproduced combining the viscoelastic Generalized Maxwell model with the Time Temperature Superimposition Principle (TTSP), enabling the definition of the relaxation properties of the material as a function of the temperature [1]. We deploy this time-dependent rheological model directly to the one-dimensional beam strain and stress measures, allowing for the derivation of a primal formulation that does not require additional unknowns compared to the case of rate independent linear elastic materials [2, 3]. High efficiency is achieved by adopting the isogeometric collocation (IGA-C) method for the spatial discretization [4]. IGA-C eliminates the need for element integration while maintaining high-order spatial accuracy and exact geometry representation typical of IGA. The model we propose supports arbitrarily curved initial geometries and employs the trapezoidal rule for the time integration. Numerical applications demonstrate the capability of the formulation to simulate complex thermo-mechanical problems in a very efficient and accurate way, paving the way to modelling shape programming and recovery of SMP beams with applications to smart materials, morphing structures and biomedical devices such as patient tailored cardiovascular stents.