Turbine inlet temperature is steadily increasing to achieve high specific thrust and efficiency of gas turbine engines. Turbine cooling technology is essential to increase turbine inlet temperature. For this study, a small or medium sized aircraft engine of 10,000 lbf class with the turbine inlet temperature of $1,400^{circ}C$, the engine overall pressure ratio of 32.2, and the bypass ratio of 5 was set as the baseline model and its performance analysis was performed at the design point. The engine has the performance of 10,013 lbf thrust and the specific fuel consumption of 0.362 lbm/hr/lbf. The thrust and the specific fuel consumption of the baseline model were compared with those of similar class engines. Based on these results, the turbine design requirements were assigned. In addition, the parametric analysis of the engine, related to aerodynamic and cooling design of the high pressure turbine, was performed. Based on the baseline model engine, the influence of turbine inlet temperature, cooling flow ratio, and high pressure turbine efficiency variations on the engine performance was analyzed.