Latent thermal energy storages (LTES) offer a high storage density within a narrow temperature range. Due to the typically low thermal conductivity of the applied phase change materials (PCM), the power of the storages is limited. To increase the power, an efficient heat exchanger with a large heat transfer surface and a higher thermal conductivity is needed. In this article, planar wire cloth heat exchangers are investigated to obtain these properties. They investigated the first time for LTES. Therefore, we developed a finite element method (FEM) model of the heat exchanger and validated it against the experimental characterization of a prototype LTES. As PCM, the commercially available paraffin RT35HC is used. The performance of the wire cloth is compared to tube bundle heat exchanger by a parametric study. The tube diameter, tube distance, wire diameter and heat exchanger distance were varied. In addition, aluminum and stainless steel were investigated as materials for the heat exchanger. In total, 654 variants were simulated. Compared to tube bundle heat exchanger with equal tube arrangement, the wire cloth can increase the mean thermal power by a factor of 4.20 but can also reduce the storage capacity by a minimum factor of 0.85. A Pareto frontier analysis shows that for a free arrangement of parallel tubes, the tube bundle and wire cloth heat exchanger reach similar performance and storage capacities.