The thermal performance of heat sinks is enhanced, in the present paper, by applying a material distribution topology optimization approach. We consider solid structures enclosed in three dimensional steady-state conductive differentially heated cavities. The algorithm iteratively updates the geometry of a heat sink, relying on gradient information. The gradient information are computed using adjoint sensitivity methods, combined with high-order accuracy direct numerical simulations. A complete conjugated problem is solved, in which we describe the effect of the solid material on the surrounding flow through the action of a Brinkman friction term in the Navier-Stokes equations, and we map the material distribution function onto the thermal conductivity and heat capacity in the energy conservation equation. Additionally, advanced filtering techniques are applied for enforcing a desired length scale to the solid structure. The success of the method is presented with a thorough physical investigation of the optimal results, which deliver a substantial increase of the heat transfer.