Lithium-ion (Li-ion) battery cooling using a phase change material (PCM)/compressed expanded natural graphite (CENG) composite is investigated, for a cylindrical battery cell and for a battery module scale. An electrochemistry model (average model) is coupled to the thermal model, with the addition of a one-dimensional model for the solution and solid diffusion using the nodal network method. The analysis of the temperature distribution of the battery module scale has shown that a two-dimensional model is sufficient to describe the transient temperature rise. In consequence, a two-dimensional cell-centred finite volume code for unstructured meshes is developed with additions of the electrochemistry and phase change. This two-dimensional thermal model is used to investigate a new and usual battery module configurations cooled by PCM/CENG at different discharge rates. The comparison of both configurations with a constant source term and heat generation based on the electrochemistry model showed the superiority of the new design. In this study, comparisons between the predictions from different analytical and computational tools as well as open-source packages were carried out, and close agreements have been observed.