The development of the additive manufacturing technology has enabled the design of components with complex structures that were previously unfeasible with conventional techniques. Among them, the Triply Periodic Minimal Surface (TPMS) structures are gaining scientific interest in several applications. Thanks to their high surface-to-volume ratio, lightweight construction, and exceptional mechanical properties, TPMS structures are being investigated for the production of high-performance heat exchangers to be adopted in different industrial fields, such as automotive and aerospace. Another significant advantage of the TPMS structures is their high degree of design flexibility. Each structure is created by replicating a characteristic unit cell in the three spatial dimensions. The three key parameters, namely cell type, cell dimension and wall thickness can be adjusted to provide considerable versatility in the design process. As for the heat exchangers, the variation of these parameters results in different values of heat transfer and pressure drop. If, on the one hand, this flexibility leads to a wide range of design possibilities, on the other hand it generates uncertainty when the most suitable cell (with the best set of parameters) has to be selected. Therefore, the aim of the paper is to address the initial challenge in the design process of an innovative heat exchanger that incorporates a TPMS structure, which is the selection of the unit cell. Based on a literature review, four TPMS structures are selected as the most promising ones for the purpose, namely Gyroid, I-WP, Primitive and Diamond. Small prototypes of the selected structures are numerically tested at laminar and turbulent flow conditions to compare their performances in terms of heat transfer and pressure drop against a more traditional solution. In order to ensure an unbiased comparison between the structures, they are compared on equal volume of the specimen, wall thickness and unit cell dimension. Finally, a compact plate heat exchanger based on turbulators is added to the comparison, to investigate the capabilities of the TPMS structures compared to a more conventional solution.