Transient heat transfer occurs in a wide array of heat exchange devices and those subjected to heat input. Effective control of heat energy during transient heat transfer is vital to increase the operating life and effectiveness of the device and equipment subjected to the heating and cooling cycle. Extended surfaces in the form of pin fins are used to augment cooling in applications like electric vehicle batteries, computers, transformers, drones, and microcontrollers. In this study, an attempt is made to examine the heating and cooling cycle, the time required to attain a target temperature, and the enhancement ratio of finned heat exchangers. The heat sink is provided with graphene nanocoating intended for electric vehicle battery cooling. The performance of the heat sink and its counterparts having two different types of pin fins, that is, circular and square, are compared. Four different heat inputs were considered, that is, 15, 25, 35, and 45 W. Three different target temperatures, that is, 46, 56, and 66°C, were accounted for during the comparison. It is concluded that the graphene nanoparticles facilitated enhanced heat transfer during the heating cycle when the input heat was 25 W and above. The square pin fins exhibited an enhancement ratio of 1.5, irrespective of the input heat energy.