Immersion-cooled battery thermal management systems (BTMSs) are generally designed and analyzed using numerical simulations. These models must couple the electrochemical and thermal-fluid physics for accurate results. However, such a numerical approach is computationally expensive and may not be feasible, particularly for large systems. Here, we develop a computationally efficient approach to study immersion cooling-based BTMSs with the coupled physics. After validating the simplified immersion-cooled battery model for fixed convection coefficient, we then define two simplified immersion cooling models: one using existing heat transfer correlations and the other employing customized correlations trained from fully-coupled numerical models.  The trained models are highly accurate (error <3%).  Moreover, they are very flexible as they can be formulated to study different combinations of mass flow rates, fluids, and discharge rates using a single heat transfer correlation. Additionally, the trained models are data-frugal, requiring only data from two mass flow rates (for a given fluid and discharge rate) to predict the response for other mass flow rates. The significant reduction in computation cost [from hours or days for the fully-coupled numerical models to seconds for proposed models] makes the proposed approach more suitable for rapid analysis, optimization, and real-time implementation of the immersion-cooled BTMSs.