Static immersion cooling (that is, immersing a hot object in a quiescent fluid) is an effective and straightforward thermal management approach useful for devices ranging from batteries to data centers. In the present work, we comprehensively evaluate static immersion cooling for lithium-ion batteries (LIBs) leveraging experimental measurements to inform data-driven models. We measure the evolution of cell voltage and temperature during discharging for three different LIBs (two commercial and one custom built with an internal thermocouple) with five different cooling fluids (four dielectric fluids and air) across various discharge rates (0.25C to 5C). While  controlling temperature rises can improve safety (avoiding thermal runaway), lower temperature rise (i.e., better cooling) leads to higher heat generation rates and lower discharge time (∝ energy supplied) due to the electrochemical kinetics, and this thermally-driven apparent capacity fade becomes more significant at higher discharge rates. For example at 5C, air cooling with a temperature rise of 53.7 K corresponds to a discharge time of 693 s and 12.5 W of heat generation, whereas cooling with deionized water yields a temperature rise of 7.6 K corresponds to a discharge time of 599 s and heat generation of 16.7 W. Moreover, the internal temperature gradient (i.e., temperature difference between the core and surface) of the cell is approximately independent of cooling fluid at low discharge rates (∼3 K for all fluids at 1.5C), even though the absolute  magnitude of temperature rise is significantly different. Further, we propose techniques to estimate the internal heat generation rates and heat transfer coefficients from the measured data. Building on this, we develop physics-based data-driven models for temperature response during charging and discharging, thus eliminating the need for large training data sizes. One method leverages conservation of energy (with cell voltage as input) to model the evolution of temperature (with error less than 1 K). The second method introduces an electrochemical model to eliminate the need for cell voltage, resulting in error of less than 0.86 K in the temperature predictions. Finally, we show the influence of the choice of fluids on LIB degradation, demonstrating that there is an optimum window of temperatures to minimize the irreversible degradation of the batteries. Ultimately, these data-efficient models provide a tool for the quick design and real-time thermal control of immersion-cooled systems.