Due to some engineering issues, experiments and simulations of performance characteristics are particularly time-consuming. Therefore, establishing a single-precision surrogate model for optimization design is too costly in terms of resources. As a result, multi-fidelity surrogate models have gradually gained widespread application. The efficient global optimization methods for multi-fidelity surrogate models face two major challenges: determining the locations of updated sample points and selecting the fidelity levels. Effective multi-fidelity infill sampling criteria can make rational use of both high- and low-fidelity data, reduce computational costs, and improve computational efficiency. To this end, this paper establishes Co-Kriging models using three numerical examples: the peak function, the Hartmann4D function, and the Ackley5 function. The models are optimized using the Generalized Expected Improvement (GEI) and Augmented-Expected Improvement (Au-EI) optimization algorithms for comparison. The results show that the GEI method can significantly reduce the number of iterations and improve computational efficiency compared to the Au-EI method. However, the Au-EI method can significantly reduce computational costs compared to the GEI method. The optimization design of battery cooling plate channels is crucial for improving battery performance and service life. This paper optimizes the design of battery cooling plate channels using both the GEI and Au-EI algorithms, providing new ideas and methods for solving complex optimization problems in this field and offering strong support for related engineering designs.