Development of load-bearing polymer composite constructions in civil engineering, such as industrial chimneys and gas ducts, requires filling some research gaps. These gaps are related to long-term behavior under mechanical and temperature loads, cyclic ones as well. Such conditions mean that viscoelasticity should be considered. First of all, viscoelastic parameters should be calculated, based on the used inner structure model. Then, due to the high working temperatures, thermal aging should be considered as well. This research is devoted to effects of thermal aging on viscoelastic behavior of polymers. Two sets of experiments were conducted: creep tensile tests and cyclic heating in constrained state. The Kelvin-Voigt viscoelasticity model was used to determine the rheological parameters of binder from experimental creep curves. Thermally-aged binder turned out to lose its viscous properties and became elastic. Cyclic heating was used to compare the behavior of normal and thermally-aged binder and to evaluate the possibility of temperature stress accumulation. Similar to creep tests, cyclic heating showed that aged binder lost viscosity and worked almost perfectly elastic. Non-aged binder was prone to stress accumulation much more. As a result, the rheological behavior of aged and non-aged binder was compared and showed a significant difference. In addition, the influence of temperature stress accumulation on stress—strain state was evaluated and turned out to be significant as well. The obtained results can be further used to predict the mechanical behavior of structures made of polymer composites operating for a long time at elevated temperatures, including those exceeding the glass transition temperature.