Truss lattice structures are intricate geometries, whose fabrication has recently been simplified by the development of Additive Manufacturing (AM) technologies. These lightweight geometries present great volume densities and surface-to-occupancy ratios, which makes them ideal for thermal dissipation applications. This paper introduces a new framework for the parametric design of graded truss lattice structures that maximize passive cooling. It exploits the results of a semi-analytic formulation and analysis of the volume density and surface-to-occupancy ratio of state-of-the-art unit cells. In particular, it comes out that any truss lattice structure presents an optimal beam diameter over unit cell size ratio that maximizes its surface-to-occupancy value. This value and the ratio for which it is reached are identified and compared for the most common unit cells. The unit cell with the maximal surface-to-occupancy ratio is then identified, along with its set of optimal parameters, taking into account additive manufacturing constraints. The validation of this optimal geometry is performed by populating pre-defined design spaces of both academic and industrial case studies. An orientation strategy and a parametric gradation approach are also proposed to further optimize the generated heat sinks and maximize passive cooling. These results are very helpful to support decision making during the parametric design of a heat sink and to identify, a priori, the optimal unit cell, its control parameters, its orientation and its gradation strategy. The generated geometries are compared with traditional heat sink structures through static heat dissipation simulations, in order to demonstrate their interest.