The improvement of the cooling performance of liquid‐cooled microchannel heat sinks used for densely packed electronic circuits is sorted via passive techniques like tuning substrate or coolant properties. We propose a design for enhancing heat sink performance by simulataneously modifying the channel geometry and tuning the fluid rheology. By modeling the coolant as a power law fluid, its rheological behavior is varied ranging from shear‐thinning to shear‐thickening, alongside Newtonian fluid. We introduced tapering to the middle wall that separates the bottom and top channels of a double layered microchannel heat sink (DL‐MCHS), causing both channels to converge. This convergence not only increases the flow velocity within the downstream microchannel but also reduces the apparent viscosity of the shear‐thinning fluid being subjected to shear, resulting in enhanced thermal and hydraulic performance. We analyze the results from both the first and the second law of thermodynamics context, demonstrating that a tapered DL‐MCHS with shear‐thinning fluid outperforms a straight partition wall DL‐MCHS with Newtonian coolant. However, we also discovered that extreme tapering compromises thermodynamic viability, but by fine‐tuning the extent of tapering, we inferred that a DL‐MCHS with shear‐thinning fluid can become viable with little compromise in the thermal performance.