This paper presents robust and reliable computational fluid dynamics (CFD) analyses to investigate water flow and heat transfer within disk-shaped micro-scale heat sinks having bio-inspired fractal-like branching channel networks. The developed computational model is initially validated using available experimental data for water flow at various Reynolds numbers within a micro-scale heat sink featuring 10 parallel straight channels. Subsequently, forced convection of water at the Reynolds numbers of 125, 250, and 500 is studied within three different micro-scale heat sink configurations. These configurations include both conventional and fractal designs, featuring straight channels in the former and fractal bifurcating channels in the latter. Computational predictions for pressure drop (ΔP) and maximum temperature gradient (ΔT_max) are compared between the fractal and conventional heat sinks. Results indicate that under identical flow rates and heat loads, the heat sink with a fractal design leads to a more uniform temperature distribution over the heated surface. Additionally, it is found that the heat sink with bifurcating channels exhibits a 25% enhancement in thermal-hydraulic performance compared to the conventional one with straight channels, despite having the same flow rate, heat transfer area, and heat load.