This paper considers the thermo-hydraulic implications of using convection channels for cooling a heat-generating disc-shaped domain. This is essentially a conjugate problem of conduction through the solid part of the domain coupled with convection through single inlet flow configurations. Four different 3D configurations are considered, comparing two tree-shaped flow networks with their equivalent radial configurations (i.e., with one inlet and the same number of outlets). All four configurations have the same solid and fluid volumes, and the same volumetric heat generation rate. Fully developed laminar and turbulent flows are considered at the inlet, with outlet Reynolds numbers ranging from 0 to 100,000, and five different solid/fluid (k^*) thermal conductivity ratios. The results show the hydraulic performance of the flow networks is strongly dependent on the number of bifurcations and on the increase in the flow strength (mass flow rate or Re number) with the bifurcations-induced pressure losses becoming comparable or larger than the pressure losses caused by the straight sections of the flow channels. Similarly, there seems to be no simple prediction of how the radial and networking configurations perform when it comes to the thermal process, with k^* being an additional parameter affecting their performances. Therefore, the determination of the configuration for best thermal and flow performances depends on characteristics beyond the fluid flow geometry.