The thermal management of a cylindrical battery cell by a phase change material (PCM)/compressed expanded natural graphite (CENG) is investigated in this study. The transient thermal behaviour of both the battery and the PCM/CENG is described with a simplified one-dimensional model taking into account the physical and phase change properties of the PCM/CENG composite. The 1D analytical/computational model yielded nearly identical results to the three-dimensional simulation results for various cooling strategies. Therefore, the 1D model is sufficient to describe the transient behaviour of the battery cooled by a PCM/CENG composite. Moreover, the maximum temperature reached by the PCM/CENG cooling strategy is much lower than that by the forced convection in the same configuration. In the test case studied, the PCM showed superior transient characteristics to forced convection cooling. The PCM cooling is able to maintain a lower maximum temperature during the melting process and to extend the transient time for temperature rise. Furthermore, the graphite-matrix bulk density is identified as an important parameter for optimising the PCM/CENG cooling strategy.