Triply Periodic Minimal Surface (TPMS) structures offer the possibility of reinventing structural parts and heat exchangers to obtain higher efficiency and lighter or even multi-functional components. The crescent global climate concern has led to increasingly stringent emissions regulations and the adoption of TPMS represents a resourceful tool for OEMs to downsize and lighten mechanical parts, thereby reducing the overall vehicle weight and the fuel consumption. In particular, TPMS structures are gaining growing interest in the heat exchanger field as their morphology allows them to naturally house two separate fluids, thus ensuring heat transfer without mixing. Moreover, TPMS-based heat exchangers can offer countless possible design configurations. These structures are obtained by periodic repetitions in the three spatial dimensions of a specific unit cell with defined dimensions and wall thickness. By tuning their characteristic parameters, the structure can be tailored to obtain the desired weight, surface-to-volume ratio and strength. In the light of this, the paper provides a numerical comparison between two different unit cell types and four different unit cell dimensions to identify the most suitable parameter combination of a water-engine oil heat exchanger exploiting a TPMS structure. Based on previous work, the Gyroid and Diamond cell types are considered as the most promising structures, while the considered cell dimensions are 5, 6, 8 and 12 mm. For a fair comparison, the specimens share the same volume and wall thickness, which is chosen to minimize thermal conductive resistance and concurrently is the minimum value required by technological and structural requirements. The specimens are tested at four mass flow rate combinations of engine oil and water, representative of an automotive oil cooler. Finally, the structures are compared in terms of the computed pressure drops and heat transfer. In addition, a plate-fin heat exchanger with turbulators is added to the comparison to discuss the potentials of this innovative structures with respect to conventional solutions.