The introduction of a high-thermal-conductivity porous medium stands as an effective strategy for enhancing the heat transfer rate within battery thermal management using phase change material (PCM). In this study, we have delved into the investigation of heat transfer augmentation in battery thermal management through the implementation of toroidal porous medium. The exploration encompasses the effects of Rayleigh numbers, thicknesses of the toroidal porous medium, different kinds of porous medium and PCM. By comparing the liquid fraction, dynamic temperature and the latent heat ratio, we found the effect of Rayleigh number and thickness of porous medium on the property of the battery thermal management. The results indicate that by applying thicker toroidal porous medium could weaken the heat accumulation derived by high Rayleigh numbers. Case of d = 0.273R exhibits superior performance for a significant portion of the entire process compared to other cases with thickness of 0.235R, 0.326R, 0.408R and uniform distributed, while the dominant position is difficult to hold due to the heat accumulation. The conclusion is universal for different porous medium and PCM materials. The optimal distribution of porous medium should seek a balance between enhancing heat conduction and weakening thermal convection. A more scattered distributed porous medium could weaken the effect of heat convection and rises the latent heat ratio.