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Electronic system layouts have increasingly become smaller and more compact. To address the growing demand for performance, dynamic thermal management with thermal energy storage has emerged as an attractive solution. Phase change materials (PCM) can store and release large amounts of heat through melting or solidification. However, they are limited by their thermal conductivity, which is several orders of magnitude lower than traditional heat sinks. To address this design weakness, we have developed a novel composite consisting of vertically aligned carbon nanotube arrays infiltrated with PCM to deliver a high thermal conductivity storage medium that also maintains the high latent heat capacity of the native PCM. This study numerically and experimentally investigates the design of an encapsulated CNT-PCM composite and its impact on the temperature rise and peak temperature of an electronic device. Different form factors have been experimentally tested. The composite's impact on a heating element is measured experimentally, and a numerical model is developed and verified using the experimental results. Additional models are designed to evaluate the effect of composite thickness on thermal response.