Porous structures have enormous potential in energy storage, thermal management, desalination, biomedicine, and catalytic reactions for their superior thermal conductivity, high specific surface area, low density, and excellent accommodation capability with volume and thermal variation. The morphology of porous structure has a significant impact on fluid flow, heat/mass transport, and strength performances. However, the available fabrication techniques are not directly capable of tailoring the porous structure with well controlled pore features and functionally graded pore morphology, limiting the performance enhancements of these systems. A triply periodic minimal surface (TPMS) provides a promising tool to customize the porous structure topology with well-controlled pore features (e.g., porosity, pore diameter, and pore density) and fabricate these parts with additive manufacturing. In this paper, porous structures with designated pore parameters were built based on the mathematically defined iWP (W) surface, primitive (P) surface, diamond (D) surface, and gyroid (G) surface. The fluid flow and heat transfer characteristics in the porous media were also examined. Simulation results confirmed the significant influence of variable physical properties on heat transfer coefficients which rapidly increased as the fluid inlet temperature approached to the pseudo-critical point.