In this paper, the flow behavior and heat transfer performance of a microchannel heat sink is examined. Microchannel heat sink is a heat exchanger that is used to control the temperature of electronic devices with high heat flux capacity. A comprehensive thermal model for a microchannel should include a three-dimensional conduction analysis in the solid parts, followed by an extensive three-dimensional developing flow in the fluid region. The heat transfer analysis in the transition region of the fluid section is a crucial matter. Hydrodynamic and thermal entrance lengths are two important parameters, among others, which are studied in the solution. To examine the potential of using a non-Newtonian fluid, the power law model was used for both Newtonian and non-Newtonian fluids. The numerical solution of the problem was based on a finite difference approach using a control volume with staggered grid system. The SIMPLE algorithm was applied to the problem, and convection terms were estimated using QUICK method. A comparison of the Newtonian and non-Newtonian results showed that for shear thinning fluids, the pressure drop could reduce up to 45%, while for shear thickening fluids, it can increase up to 48%. The same comparison for the Nusselt number showed about a 160% increase with shear thinning fluids and a 43% decrease with shear thickening fluids. The thermal resistance at a Reynolds number of 50 will reduce approximately 25% with shear thinning fluids and will increase approximately 5% with shear thickening fluids. At higher values of the Reynolds number, the changes in the value of the thermal resistance are more pronounced.