The new possibilities offered by additive manufacturing (AM) can be exploited in gas turbines to produce a new generation of complex and efficient internal coolant systems. The flexibility offered by this new manufacturing method needs a paradigm shift in the design approach, and a possible solution is offered by topology optimization. The overall goal of this work is to propose an innovative method to design internal channels in gas turbines that fully exploit AM capabilities. The present work contains a new application of a fluid topology sedimentation method to optimize the internal coolant geometries with minimal pressure losses while maximizing the heat exchange. The domain is considered as a porous medium with variable porosity: the solution is represented by the final solid distribution that constitutes the optimized structure. In this work, the governing equations for an incompressible flow in a porous medium are considered together with a conjugate heat transfer equation that includes porosity-dependent thermal diffusivity. An adjoint optimization approach with steepest descent method is used to build the optimization algorithm. The simulations are carried out on three different geometries: a U-bend, a straight duct, and a rectangular box. For the U-bend, a series of splitter is automatically generated by the code, minimizing the stagnation pressure losses. In the straight duct and in the rectangular box, the impact of different choices of the weights and of the definition of the porosity-dependent thermal diffusivity is analyzed. The results show the formation of splitters and bifurcations in the box and “riblike” structures in the straight duct, which enhance the heat transfer.