In this study, a coupled numerical computation approach integrating aerothermal and thermomechanical effects was employed to investigate the cooling efficiency and thermal stress characteristics of gas turbine stator blades. A comprehensive analysis was conducted considering varying turbulence intensities in the coolant flow (spanning from 0.05 to 0.15) and different coolant media configurations, including pure air, dual-medium mixture of air and steam, and pure steam. The distributional traits of cooling efficiency and thermal stress on the stator blade surface under these conditions were meticulously examined. Furthermore, quantitative assessments were performed to determine the extent to which coolant turbulence intensity and coolant type affect the average cooling efficiency and maximum equivalent thermal stress of turbine stator blades, thereby revealing the influence laws. The results reveal that the minimum cooling efficiency on the stator blade surface predominantly occurs at the position of channel 4 on the pressure surface, while the highest cooling efficiency is generally found near the leading edge of the suction surface. Regions of elevated thermal stress were consistently concentrated around the stator blade tip and root areas. When the coolant turbulence intensity increased from 0.05 to 0.15, the average cooling efficiency on the stator blade surface improved by 2.06%, accompanied by a reduction of 1.12% in the maximum thermal stress. In comparison to pure air cooling, dual-medium (air and steam) cooling and pure steam cooling lead to respective enhancements in the average cooling efficiency of approximately 3.3% and 13.2%, with corresponding decreases in the maximum thermal stress of 2.18% and 10.2%.