In this paper, first we investigated the effects of the amount of crushed basalt aggregates on the compressive strength, flexural strength, and splitting tensile strength of a polymer concrete (PC) obtained by epoxy resin. We found that increasing the amount of epoxy resin to the basalt aggregates to 25 wt% improved mechanical properties of the concrete. After determining the optimum weight percentage of basalt in epoxy, the mechanical properties of the optimized PC were experimentally investigated at three different temperatures: 50°C, 75°C, and 100°C. Our results indicate that as the temperature increases, the highest maximum stress rapidly decreases, but the yield displacement increases significantly. Moreover, the PC sample became barrel shaped under compression stress because of its ductility at high temperatures. Afterwards, effects of four different aggregate sizes, 3–5 mm, 1.2–3 mm, 0.6–1.2 mm, and microsized particles, on mechanical properties of the optimized PC were experimentally studied. We found that, the larger aggregate size outcomes higher compressive strength and lower flexural and splitting tensile strength. Finally, an empirical model for the relationships between compressive, splitting tensile, and flexural stress was derived that can be used to predict the strength of PCs.