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Phase change materials (PCMs) have tremendous capacity as passive components to recover and repurpose thermal energy from transient power systems. However, PCMs are only effective if the time scale of the thermal energy storage and retrieval rates match those required for a particular system. We develop a framework to assess the efficiency of pulsed thermal energy storage based on the concept of “thermal impedance,” drawing upon an analogous approach from electrical energy storage. We experimentally characterize a 1 cm thick paraffin-infiltrated copper foam composite PCM subject to pulsed heat boundary conditions up to 1 W cm−2 and demonstrate a decrease in thermal impedance by up to a factor of 2.5× in the regime in which melting occurs (τon = 10−1 to >102 s) relative to a reference case in which melting does not occur. This represents both a signature of the ability to extract or retrieve thermal energy via latent heat, as well as an experimentally accessible measure that provides insight into the internal dynamics of a composite PCM volume. These principles can serve to design the internal structure of composite PCM elements for pulsed thermal systems.