The generation of heat within the rechargeable batteries during the charge–discharge cycles is inevitable, making heat dissipation a very critical part of their design and operation procedure, as a safety and sustainability measure. In particular, when the heat gets the least possibility to escape from the electrode surface, the boundary of the packaging material remains the sole heat dissipator. In this regard, the heat gets accumulated in the central zone, making it the most critical, since it has the least possibility to escape to the surroundings. Anticipating such a heat trap, a central heat sink component is devised, where the role of its conductivity and the relative scale is analyzed based on the formation of transient and steady-state temperature profiles. Additionally, an analytical solution is attained for the location of the maximum temperature, where its value and correlation with the electrolyte conductivity, heat generation rate, and scale of the cell have been quantified. Due to the existence of the curved boundaries, it is shown that the time versus space resolution for capturing the transient evolution of the temperature is more strict than the flat surface and analytically acquired as ≈33% smaller value. Such enhanced design and subsequent analysis are critical for planning sustainable and cost-effective packaging to avoid the ignition and failure of the respective electrolyte.