The rapid expansion of the electric vehicle (EV) industry necessitates the development of advanced battery thermal management systems (BTMSs) to safeguard the cyclic properties and security of lithium-ion batteries. However, the assessment of the performance of BTMS often overlooks the importance of considering not only the thermal regulation effectiveness on batteries but also its own energy efficiency. This study investigated the synergistic effects of BTMS design and control strategies on both thermal performance and energy utilization of its own. A multiphysics-based model was developed, featuring an 18,650 Lithium-ion battery module with curved cooling channels, to systematically evaluate the impact of cooling channel width and warping angle, inlet coolant temperature and velocity, and charging rate on system performance and efficiency. To further expedite the design optimization process, a Gaussian process (GP)-based surrogate model was implemented. An uncertainty quantification analysis was subsequently performed to validate the robustness of the optimized designs against stochastic variations. The findings indicate that the channel width and coolant velocity play a pivotal role in enhancing BTMS efficiency. Through a rigorous multi-objective optimization process, the energy efficiency was improved by 126 %, while maintaining battery temperatures below 28.4 °C and coolant pressure drops under 3.6 kPa. The integration of multiphysics simulation and machine learning assisted optimization technique represents a pioneering step forward in the development of sophisticated and efficient BTMS solutions for future electric vehicles.