In this research, we developed a graph-based framework to represent various aspects of optimal thermal management system design, with the aim of rapidly and efficiently identifying optimal design candidates. Initially, the graph-based framework is utilized to generate diverse thermal management system architectures. The dynamics of these system architectures are modeled under various loading conditions, and an open-loop optimal controller is employed to determine each system's optimal performance. These modeled cases constitute the dataset, with the corresponding optimal performance values serving as the labels for the data. In the subsequent step, a Graph Neural Network (GNN) model is trained on 30% of the labeled data to predict the systems' performance, effectively addressing a regression problem. Utilizing this trained model, we estimate the performance values for the remaining 70% of the data, which serves as the test set. In the third step, the predicted performance values are employed to rank the test data, facilitating prioritized evaluation of the design scenarios. Specifically, a small subset of the test data with the highest estimated ranks undergoes evaluation via the open-loop optimal control solver. This targeted approach concentrates on evaluating higher-ranked designs identified by the GNN, replacing the exhaustive search (enumeration-based) of all design cases. The results demonstrate a significant average reduction of over 92% in the number of system dynamic modeling and optimal control analyses required to identify optimal design scenarios.