In this paper, thermal management in GaN (gallium nitride) based microelectronic devices is addressed using microfluidic cooling. Numerical modeling is done using finite element analysis (FEA), and the results for temperature distribution are presented for a system comprising multiple cooling channels underneath GaN high-electron mobility transistors (HEMTs). The thermal stack modeled is compatible for heterogeneous integration with conventional silicon-based CMOS devices. Parametric studies for cooling performance are done over a range of geometric and flow factors to determine the optimal cooling configuration within the specified constraints. A power dissipation of 2–4 W/mm is modeled along each HEMT finger in the proposed configuration. The cooling arrangements modeled here hold promising potential for implementation in high-performance radio-frequency (RF) systems for power amplifiers, transmission lines, and other applications in defense and military.