Thermal management and energy storage problems often utilize extended surfaces, also known as fins for enhanced heat transfer. While thermal conduction is usually the dominant mode of heat transfer in a solid fin, the use of porous fins that include advective thermal transport due to porous fluid flow has also been investigated. In particular, the steady state thermal performance of a porous fin with pressure-driven radially outwards flow has been studied. While such results are helpful for studying problems that are inherently steady state in nature, such results do not readily apply to problems where heat removal or energy storage occurs only over a short period of time. This work presents transient thermal analysis of a porous fin with radial porous fluid flow driven by a pressure gradient. It is shown that the transient temperature field in the fin is governed by a transient convection-diffusion-reaction (CDR) equation, the solution for which is derived in the form of Bessel functions. Based on this solution, the evolution of fin performance with time is examined. Comparison of heat removed by the porous fin with a baseline case without any fin is carried out. The time taken to reach steady state is calculated. Key non-dimensional parameters appearing in this problem are identified and their impact on fin performance over time is investigated. Since fin porosity improves advective thermal transport but suppresses diffusive transport at different rates at different times, therefore, it is shown that for a given operating time, there may exist an optimal porosity that maximizes the rate of heat removal. It is shown that the operating time period of the fin plays a key role in determining whether fin porosity strongly impacts heat removal rate or not. Consequently, it is shown that it is important to consider transient effects in determining whether the use of a porous fin is beneficial at all, and, if so, what is the optimal fin porosity to use. This work contributes towards porous fin theory, and offers practical design guidelines for improving and optimizing the transient performance of porous fins.