In the present research, the authors have attempted to examine the compressive strength of conventional concrete, which is made using different aggregate sizes and geometries considering various curing temperatures. To this end, different aggregate geometries (rounded and angular) were utilized in various aggregate sizes (10, 20, and 30 mm) to prepare 108 rectangular cubic specimens. Then, the curing process was carried out in the vicinity of wind at different temperatures (5 °C < T < 30 °C). Next, the static compression experiments were performed on 28-day concrete specimens. Additionally, each test was repeated three times to check the repeatability of the results. Finally, the mean results were reported as the strength of concrete specimens. Response Surface Analysis (RSA) was utilized to determine the interaction effects of different parameters including the appearance of aggregates (shape and size) and curing temperature on the concrete strength. Afterwards, the optimum values of parameters were reported based on the RSA results to achieve maximum compressive strength. Moreover, to estimate concrete strength, a back-propagation neural network (OBPNN) optimized by a genetic algorithm (GA) was used. The findings of this study indicated that the developed neural network approach is greatly consistent with the experimental ones. Additionally, the compressive strength of concrete can be significantly increased (about 30%) by controlling the curing temperature in the range of 5–15 °C.