The cooking performance of the solar box cooker (SBC) is enhanced by utilizing magnesium chloride hexahydrate (MgSO4·7H2O) with plastic balls (PBs) encasing the phase-change material (PCM). Accurate predictions of SBC efficiency were achieved using an Artificial Neural Network (ANN) simulation and the incorporation of thermal behavior utilizing the tree-seed metaheuristic algorithm (TSA). Therefore, improving ANN performance may be necessary to reap the benefits associated with adopting a variation in engineering design. The design incorporates a copper bar plate (CBP) that is 50% larger than a silver bar plate (SBP), and the Tree-Seed Algorithm (TSA) is used to establish an optimal influence for neurons. For the SBC with CBP design, food cooking efficiency was functional, with R 2, RMSE, MRE, and MAE values of 0.990, 0.0475, 0.228, and 0.050, respectively. Similarly, for SBP, the values are 0.98, 0.086, 0.007, and 0.053, respectively, simulated using the ANN/TSA technique. For the CBP in the training set “R,” testing set “R,” and overall set “R,” the respective values were 0.999, 0.995, and 0.997. Similarly, for the SBP in SBC cooking performance, the values were 1.000, 0.964, and 0.996. The performance of CBP in the SBC design with PCMPBs is found to enhance cooking efficiency, improving the system’s ability to prepare rice and eggs within 2 to 3 h.