In this work, we extend our heat transfer performance study on our proposed new and novel 3D printable architected heat sinks with geometrically complex structures based on triply periodic minimal surfaces (TPMS). Computational fluid dynamics (CFD) modeling is used to assess the effect of porosity distribution, heat load, and isothermal boundary condition on the performance of the proposed TPMS-based heat sinks in active cooling using natural and forced convection heat transfer environments. The convection heat transfer coefficient, surface temperature, pressure drop are predicted using CFD method. The CFD model is validated using experimental results for the pressure drop and is verified by standard analytical results. Three TPMS structures are investigated in different orientations. Dimensionless heat transfer groups are developed to globalize the heat transfer performance of the proposed heat sinks.