The complex aero-thermal coupling between fluid and solid regions within high-pressure turbines makes it important to perform multidisciplinary design optimization of high-pressure turbine blades. However, most published works failed to consider the correlations between blade profiles and cooling structures that could best compromise the aerodynamic and thermal performance of high-pressure turbine blades, and the related optimization problems were so far limited to single- or bi-objective ones. The critical drawbacks of these available studies are mainly due to the reduced accuracies of the adopted methods when dealing with large numbers of design variables and objectives. To tackle these difficulties, a dimension reduction-based multidisciplinary design optimization method is proposed and validated through an aero-thermal design optimization of the NASA-C3X vane with a total of 39 design variables and five performance objectives. The main novelties of this proposed method lie in a hybrid dimension reduction of design space by means of the proper orthogonal decomposition and global sensitivity analysis methods, as well as the integration of the ensemble surrogate model and the reference vector evolutionary algorithm for optimal solutions. The results show that the prediction accuracy of the ensemble surrogate model for each performance objective is enhanced, even though the dimensionalities of design space are reduced. Complicated compromises exist among the five performance objectives under consideration. For NASA-C3X vane, the optimal design helps reduce irreversible flow losses especially wake losses while reducing the volumes with high-temperature and high-temperature gradient near the trailing edge is mainly responsible for the reduced irreversible losses due to heat transfer. The outcomes of this work are particularly relevant for the advanced design optimization methods for high pressure turbines.