The industry shift to multi-core microprocessor architecture will likely cause higher temperature non-uniformity on chip surfaces, exacerbating the problem of chip reliability and lifespan. While advanced cooling technologies like two phase embedded cooling exist, the technological risks of such solutions make conventional cooling technologies more desirable. One such solution is remote cooling with heatsinks with sequential conduction resistance from chip to module. The objective of this work is to numerically demonstrate a novel concept to remotely cool chips with hotspots and maximize chip temperature uniformity using an optimized flow distribution under constrained geometric parameters for the heatsink. The optimally distributed flow conditions presented here are intended to maximize the heat transfer from a non-uniform chip power map by actively directing flow to a hotspot region. The hotspot-targeted parallel micro-channel liquid cooling design is evaluated against a baseline uniform flow conventional liquid cooling design for the industry pressure drop limit of approximately 20kPa. For an average steady-state heat flux of 145 W/cm2 on core areas (hotspots) and 18 W/cm2 on the remaining chip area (background), the chip temperature uniformity is improved by 10%. Moreover, the heatsink design has improved chip temperature uniformity without a need for any additional system level complexity, which also reduces reliability risks.