Ascertaining the uncertainty in the aerothermal performance of blade tips is crucial, as it represents the most delicate component of modern gas turbines. In this research article, a novel and efficient approach is proposed for quantifying uncertainties in aerothermal performance using a combination of universal kriging, polynomial chaos expansions, and Smolyak sparse grid technology. This method was applied to investigate the aerothermal performance of a high-pressure gas turbine rotor blade tip with high-dimensional robustness. The outcomes of the uncertainty quantification calculation reveal that the downstream total pressure loss coefficient and leakage flowrate increase under normal-speed (subsonic) and high-speed (transonic) conditions. The key uncertainty input that affects the aerodynamic performance of normal-speed and high-speed squealer tip is inlet total pressure fluctuation, with a variance index on the leakage flowrate of normal-speed and high-speed squealer tip of up to 73.92 and 83.85%, respectively. The study suggests that it is more important to control the operating conditions fluctuation than the cavity depth machining accuracy for aerodynamic performance robustness, which applies to both normal-speed and high-speed squealer tips. In line with the aerodynamic performance, the heat flux of normal-speed and high-speed squealer tip increases during operation. Notably, the sensitivity of high-speed squealer tip aerodynamic performance to operating condition fluctuations increases compared to the normal-speed squealer tip, necessitating active intervention for fluctuations in operating conditions at a higher cost for the high-speed squealer tip. The sensitivity analysis results indicate that the inlet total temperature fluctuation is the key parameter that controls the normal-speed and high-speed squealer tip heat flux uncertainty. Finally, it is worth noting that while the use of ribs can effectively enhance the robustness of blade tip heat transfer performance, the heat flux near the root of the ribs fluctuates significantly, which may further increase the thermal fatigue tendency in this region during actual operation.