Batch combustion in wood log stoves is a promising application for latent heat storage (LHS), due to the transient heat production with high peak effects. The current study aimed at designing a compact, passive and durable LHS system storing a substantial part of the heat release during batch combustion and effectively releasing the stored heat to the room for 6 to 10 hours after the last batch. The LHS system consists of a coaxial cylinder located at the top of the wood stove, replacing part of the regular stovepipe. Internal metallic fins were applied as heat transfer enhancement to homogenize the temperature distribution inside the PCM. The effect of radial fin lengths was numerically investigated through a parametric study using five different fin lengths within the PCM. Using 35-mm fins in the 70-mm PCM layer yielded the best trade-off for the application. This configuration enabled achieving a slow but close to complete melting of the PCM within a realistic combustion duration, while avoiding overheating the PCM above its degradation temperature. Thereafter, the discharge allowed releasing the stored latent heat for 6 hours. The exhaust gas inlet temperature proved to have a strong influence on the PCM thermal performance.