The demand for high-performance electric vehicles keeps increasing with the booming electric vehicles market. Thus, battery cooling is significant in enabling the battery to work under harsh discharge process. Thanks to its high efficiency and low cost, indirect liquid cooling is a widely used cooling method for batteries. Researchers are trying to optimize the plant or control design separately for a better cooling effect. However, they can only produce suboptimal results with low efficiency. Motivated by the imperfections of existing battery cooling systems, we aim to lower the cost of indirect liquid cooling for batteries considering the plant design and control design using data-driven co-design optimization. First, a finite element model of the battery was built to predict the temperature and validate our findings against experimental data. Then, a Gaussian process-based surrogate model combined with Monte Carlo simulation extended the prediction to many scenarios under harsh discharge process. Finally, the surrogate model obtained the optimal plant and control designs. The finite element model validated the optimal design, which lowered the cost by 10%.