The significant amount of heat generated during the discharge process of a lithium-ion battery can lead to battery overheat, potential damage, and even fire hazards. The optimal operating temperature of a battery ranges from 25 °C to 45 °C. Hence, battery thermal management cooling techniques are crucial for controlling battery temperature. In this work, the cooling of 21700 lithium-ion batteries during their discharging processes using phase-change materials (PCMs) and porous pure copper foams were simulated. The effects of discharge intensities, battery orientations, and battery arrangements were investigated by observing the changes in temperature distributions. Based on current simulations for a 2C discharge, air-cooled vertical batteries arranged in unidirectional configuration exhibit an increase in heat dissipation by 44% in comparison to the horizontal batteries. This leads to a decrease in the maximum battery temperature by about 10 °C. The use of either PCMs or copper foams can effectively cool the batteries. Regardless of the battery orientation, the maximum battery temperature during a 2C discharge drops dramatically from approximately 90 °C when air-cooled to roughly 40 °C when the air is replaced by PCM cooling or when inserted with a copper foam of 0.9 porosity. If the PCM/copper foam approach is implemented, this maximum temperature further decreases to slightly above 30 °C. Although not very significant, it has been discovered that crossover arrangement slightly reduces the maximum temperature by no more than 1 °C. When a pure copper foam with a porosity ranging from 0.90 to 0.97 is saturated with a PCM, the excellent thermal conductivity of pure copper, combined with the PCM latent heat absorption, can best help maintain the battery pack within its range of optimal operating temperatures. If the porosity of the copper foam decreases from 0.95 to 0.5, the volumetric average temperature of the batteries may increase from 30 °C to 31 °C.