Compared with the thermal efficiency of a conventional heat sink having an identical plate surface area and non-branching, uniform cross-section channels, the thermal efficiency of a heat sink employing a branching channel flow network can be enhanced more than 40 percent, depending upon the foot print of, and channel spacing in, the heat sink. Water was used as the working fluid in the present the analysis and its properties evaluated at 325K. Resistances through the solid material were neglected. The branching channel network is fractal-like in nature with an increase in the total flow area following a channel bifurcation and characterized by an equation used to describe the highly efficient mammalian circulatory and respiratory systems. The primary contribution to this higher thermal efficiency is attributed to a decreased input pumping power. A decrease in cross-sectional thermal resistance in the direction of flow results from channel bifurcation and is attributed to an increase in both the total channel surface area and the heat transfer coefficient, an effect most pronounced under developing flow conditions. The decreasing thermal resistance in the direction of flow is anticipated to yield a more uniform surface temperature distribution for constant heat-flux boundary conditions.