This work is concerned with the development of a framework for the efficient design of cooling channels via two different topology optimization paradigms: a diffuse and a sharp. Each approach relies on a distinct thermo-fluid modeling and features a specific material distribution mode, i.e. fraction-based (diffuse) versus interface-based (sharp). The two models are described and the corresponding solvers are validated. A gradient-based optimization methodology is adopted and the details of the adjoint-based gradient computation are introduced. Finally, examples of cooling channel design optimization are presented and discussed.