One of the key trends affecting the future of the construction industry is the issue of ecology; therefore, current activities in construction aim to reduce the use of raw materials, which is made possible by including recycled materials in composites, among other methods. This article describes the results of tests conducted using four types of epoxy composites, i.e., composites modified with waste rubber (WR), composites modified with waste polyethylene (PE) agglomerate, glycolysate obtained using polyethylene terephthalate (PET) waste, and control unmodified mortars (CUM). Selected properties of the mortars were monitored during their maturation under laboratory conditions, as well as after post-curing at elevated temperatures in the range of 60 °C–180 °C. With the increase in the reheating temperature, an increase in the flexural strength of all types of mortars was noted, with the highest more than twofold stronger than the unmodified composites. The compressive strength increased up to a temperature of 140 °C, and then decreased slightly. The highest value of 139.8 MPa was obtained using PET mortars. Post-curing also led to a slight loss of mass of all samples in the range of 0 to 0.06%. Statistical methods were employed, which made it possible to determine the post-curing temperature and composite composition for which the determined properties are simultaneously the most beneficial, especially for the prefabricated elements.