With the extremely rapid progress in developing new micro- electrical devices and the urgent need to harvest and store energy, thermal control and the design of a new generation of energy storage materials have grown in importance. Thermal control issues appear in designing small size electronic chips, which are subjected to high heat generation densities, and in controlling space vehicles from the excessive aerodynamic heating. In designing a thermal protection system of such application, selecting the material is a very important issue. The material used should have high specific heat with high thermal conductivity to be able to absorb and diffuse heat quickly. One of the present cooling methods in engineering systems is the usage of materials with capability of phase change in sufficient temperature range for cooling the specified piece of the device. These materials are named as phase change material or PCM, and they are ones with large latent heat which are used for great energy absorption in constant temperature having phase change as absorbing energy. To this end, investigation of inactive cooling which uses PCM as coolant in Lithium- Ion Batteries will be discussed in this work. Positive point of all PCMs is due to the large special and latent heat in these devices. On the other hand, low heat conduction coefficient is negative point in almost all PCMs. Low heat conduction of PCMs would result in increasing the response time. To overcome the low heat conduction coefficient, fins are used in this study; also we have investigated the arrangement of fins. ANSYS-FLUENT software is used for numerical simulation of the problem with Solidification Melting solver in axial symmetry manner. The results of comparison of the air cooling and cooling by materials with phase change capability show that battery cooling operation has been improved by using the material with phase change capability for the specific time range in which these materials have not completely been molten. On the other hand, the variation heat transfer coefficient of natural convection around the battery does not affect the improvement of battery cooling with use of material with phase change capability. Also the use of fins would result in improvement of the battery cooling operation in comparison to the state in which no fin is used. Moreover, as the height of fins increase the operation of battery cooling with use of materials with phase change capability will improve. Keywords: Phase change material, Latent heat thermal energy storage, Heat sink, Thermal conductivity, Fins, Solidification and Melting.