Using the SST k-ω turbulence model, a comprehensive numerical investigation was conducted to analyze the flow and heat transfer characteristics of steam within an isosceles trapezoidal cooling channel with pin-fin arrays modeled from the trailing edge of a F-class gas turbine high-temperature blade. The influence laws of various parameters, including the Reynolds number (Re, from 10,000 to 50,000), dimensionless pin-fin diameter (d/H, from 0.4 to 0.8), and dimensionless pin-fin spacing (S/H, from 1.6 to 2.4), on the flow and heat transfer performance of the isosceles trapezoidal cooling channel with pin-fin arrays were examined. Sensitivity analysis was employed to determine the relative significance of these influence parameters on the cooling performance of the isosceles trapezoidal channel with pin-fin arrays. Finally, the corresponding heat transfer and friction correlations within the investigated parameter range were developed. The research findings reveal that under different Reynolds numbers, as the dimensionless pin-fin diameter increases from 0.4 to 0.8, the friction factor within the isosceles trapezoidal cooling channel with pin-fin arrays increases by a factor of 3.25 to 3.41, while the overall average Nusselt number improves by 31.05% to 37.41%. Conversely, when the dimensionless pin-fin spacing increases from 1.6 to 2.4, the friction factor within the isosceles trapezoidal cooling channel with pin-fin arrays decreases by 67.38% to 69.18%, accompanied by a reduction in the overall average Nusselt number by 24.95% to 31.14%. When both the flow performance and heat transfer performance are taken into account, the importance of the influence parameters ranks as follows: Reynolds number, pin-fin diameter, and pin-fin spacing. It also suggests that smaller pin-fin diameters and larger pin-fin spacing should be selected in the design stage based on the variation laws of integrated thermal-hydraulic performance. The results may provide valuable references and insights for the design of steam cooling structures within high-temperature turbine blade trailing edge channels in advanced gas turbines.