Abstract Triply Periodic Minimal Surface (TPMS) possesses diverse morphological characteristics, such as pore sizes, porosity, and structural types. Integrating TPMS-based microchannels into micro-cellular cooling structures is advantageous for designing and controlling fluid characteristics within mold cooling channels. However, it is still difficult to design multi-morphology TPMS-based cooling microchannels that conform to the external shapes of injection molds. This work proposes a three-dimensional (3D) multi-morphology TPMS-based design method that transforms 3D constraints into a combination of two-dimensional (2D) constraints. Firstly, a beta growth algorithm based on closed-loop constraints is proposed to transition different morphologies smoothly on the plane. Subsequently, a transition optimization algorithm along the normal direction of the plane is introduced to smoothly transition multi-morphology TPMS-based microchannels in all directions. With this layered approach, multi-morphology microchannels can be obtained with first-order geometric continuity under complex shape constraints. Finally, several TPMS-based conformal cooling structures are designed for an automotive hood cover. The results of finite element simulations show that the cooling structures generated by the proposed method have a better cooling effect than the conformal channels. It can be concluded that multi-morphology TPMS-based structures perform better by contrast with conformal channels as the average temperature of the cooling surface decreases by 8.48K, and the standard deviation of temperature distribution decreases by 24.65%.