Additive manufacturing enables highly efficient cooling fabrications such as triply periodic minimal surface (TPMS), which provides excellent heat transfer per unit volume. In a wedge-shaped channel representing trailing edge turbine blade cooling, conventional pin fins are replaced with different TPMS structures due to their topological features to enhance the flow mixing and heat transfer, strengthen the structural integrity, and reduce the manufacturing material. The turbulent flow and heat transfer characteristics of solid- and sheet-based TPMS models, including gyroid, diamond, and Schoen-I-graph and wrapped package (IWP), are numerically investigated. The heat transfer, pressure loss, and thermal performance are compared at Reynolds numbers of 10,000–30,000. Notably, among the studied TPMS structures, the diamond-sheet structure is selected as the optimal model. Compared to the baseline pin fin structure at an equal Reynolds number, it remarkably increases the overall heat transfer by up to 163.2%, the pressure loss by 181.8%, and the thermal performance by up to 77.3%. The numerical results indicate that the gyroid- and diamond-sheet structures effectively organize and interact with the cooling fluid, reducing low-velocity recirculation flow in the tip region of the trailing edge. The flow in the diamond-sheet network is distributed more evenly from the root to the tip region, improving the temperature uniformity throughout the channel. Overall, the diamond-sheet TPMS structure could effectively improve the heat transfer performance, temperature uniformity, and structural integrity in the turbine blades' trailing edge, thereby potentially extending the durability of the turbine blades.