This study goes beyond the common microchannel cooling system composed of uniform parallel straight microchannels and proposed a three-stage design approach for spatially thermal-aware microchannel cooling of 2D multicore processors. By applying effective strategies and arranging key design parameters, stronger cooling is provided under the high power core area, and less cooling is provided under the low power cache area to effectively save the precious pumping power, lower the hot spot temperature and lower temperature gradients on chip. Two microchannel cooling systems are specifically designed for a 2 core 150 W Intel Tulsa processor and an 8 core 260 W (doubled power) Intel Nehalem processor with single phase HFE7100 as coolant. For the Tulsa processor, a strategy named strip-and-zone is used. The final design leads to 30 kPa pressure drop and 0.094 W pumping power while maintains the hot spot temperature to be . For the Nehalem processor, a split flow microchannel system and a widen-inflow strategy are applied. A design is achieved to cost 15 kPa pressure drop and 0.0845 W pumping power while maintains the hot spot temperature to be . The design approach in this study provides the basic guide for the industrial applications of effective multicore processor cooling using microchannels.