Low thermal conductivity is a significant issue for the deployment of phase change based thermal energy stores. A structured methodology is required to find the best overall design, in order to assess its techno-economic feasibility. In this study the optimised structural configuration of graphite composites for this purpose are first considered from three different perspectives using both experimental measurements and numerical simulations. Both steady state and dynamic performance are taken into account, with the latter being considered both with and without phase change. In all three cases it is demonstrated that thin, parallel graphite sheets offer the most optimal results compared to other options. Resulting in the highest composite thermal conductivity measured to date at a loading of 3.5 mass%. The next step in achieving the best overall performance is the optimisation of this composite in the context of a plate and frame heat exchanger. For this purpose a simplified analytical model of this configuration was developed and validated. This was used in conjunction with the log mean temperature difference approach to optimise the exchanger for two typical applications: low temperature, low duty and high temperature, high duty. The results indicate that, even under an idealised configuration, the system will only be suitable for high temperature applications with gas heat transfer fluids and short discharge times (~1 h). For low temperature applications it may be possible to use liquid heat transfer fluids but also only for short discharge times. From an economic perspective, the range of graphite sheets currently available on the market will have to be reduced in cost by two or more orders of magnitude in order to be cost-effective.