Glazing selection is a key strategy for improving building energy performance; however, its application in heritage buildings with architectural preservation constraints remains to be explored. This study addresses this gap by evaluating 11 glazing configurations, including single, double, and triple-pane systems with varying U-values (0.78–5.82 W/m²K), Solar Heat Gain Coefficients (0.31–0.90), and Visible Transmittance values (0.43–0.91), in a historic courtyard building located in Tehran’s hot-dry climate. Dynamic simulations were conducted using DesignBuilder, based on a Typical Meteorological Year (TMY) weather file for Tehran (Mehrabad station). The model was validated using ASHRAE Standard 140 (BESTEST) benchmark cases. Results show a consistent seasonal pattern across scenarios, although significant differences emerged during peak heating and cooling periods. The triple-pane low-E argon-filled glazing (T2) achieved the best performance, reducing annual energy consumption by 12.7% compared to the base case. In contrast, the single-pane low-iron glazing (S3) increased the energy demand by 1.2% owing to higher solar heat gains. The sensitivity analysis of building orientation indicated that the total annual energy consumption varied between approximately 85,847 kWh and 91,967 kWh, with the lowest demand observed at a 180° orientation. The economic analysis showed that the D4 double Low-E glazing system achieved a shorter payback period of approximately 6 years, whereas T2 required about 10.7 years to recover the initial investment. Overall, the findings demonstrate that reducing the U-value and Solar Heat Gain Coefficient is the most effective strategy for improving building energy performance in hot-dry climates, particularly for heritage buildings, where design modifications are limited.