This article proposes a fast charging management strategy for lithium-ion batteries and cooling systems, tackling the challenge of achieving fast charging under multiple physical constraints while minimizing cooling energy consumption and battery aging. The complex coupling between the battery and cooling system is formulated as a Stackelberg game-based bilevel optimization framework, reflecting the sequential interactions of the charging and cooling processes. To address this, a Stackelberg game-based soft actor-critic deep reinforcement learning method is developed, with rigorous proof of convergence ensuring its reliability. Extensive experimental results validate the method, showing its superiority over state-of-the-art strategies, including single-agent deep reinforcement learning, Bayesian methods, and constant current−constant voltage (CCCV)−proportional integral derivative (PID) control. This approach achieves safe, energy-efficient fast charging, offering an effective solution to balance performance, energy use, and battery longevity.