Branched or tree-shaped networks of microchannels are often preferred heatsink designs for microelectronic cooling due to their ability to offer a substantially large surface area-to-volume ratio. Designing an optimized tree-shaped heatsink in terms of hydrothermal performance poses challenges due to the intricate geometry and small-scale fluid–structure interactions involved, making prototyping challenging. We propose a systematically designed microchannel network heat exchanger inspired by tree branching patterns, aiming for ease in rapid prototyping and improved flow distributions offering enhanced thermal performance. Starting from a simpler geometrical consideration, we systematically improve the design by introducing a pin fin at the junction for improved flow distribution and then by imparting a converging angle in the channel for enhanced thermal performance. Additionally, we conduct an entropy generation analysis to examine the thermal performance of various nanofluid concentrations within the proposed device and witness significant thermal performance improvement that can benefit the thermal management of microelectronic components and other cooling applications.