The ability to enhance heat transfer rates of shear-thinning fluids in microchannel devices is evaluated numerically for steady and time-dependent flows in the range of 400 < Re < 2000. The geometry used represents a simplified micro pin-fin heat sink device with a staggered circular pin arrangement. The working fluids are composed by water and ethylene-glycol with different kinds of nanoparticles and concentrations. Four Newtonian and five non-Newtonian nanofluids are evaluated in detail, focusing on their rheological behavior, the heat extraction capacity, and the fluid dynamics developed for each flow condition. The nanofluids studied are extracted from experimental articles, and they are characterized as shear-thinning power-law ones with power-law indexes in the range 0.4946 <n < 0.69. Comparisons of heat-flux between the inlet and the outlet of the microchannel are investigated for nine different Reynolds numbers. Additionally, the pressure drop was evaluated for each case. The results show that the shear-thinning behavior of the nanofluids is the most critical factor in enhancing heat transfer rates due to the promotion of unsteady flows even for low Reynolds number values and a reduction of pressure drop. A large number of numerical tests are presented and carefully analyzed to justify our claims.