Abstract Electronic devices experience spatial variation in power dissipation, which results in high-temperature hot spots. These locations require aggressive thermal management, which can be complex and costly. Simple solutions such as single-phase micro-channels can provide adequate heat transfer, but they are not designed to control heat transfer locally. However, micro-channels can be tailored to control local flow rates and heat transfer, potentially mitigating hot spot temperatures. Using a conductive and convective resistance network for a micro-channel, an analytical model is generated for heat transfer within an individual passage. For a given channel width, this model relates the channel depth to its resistance through a power law. Over a wide range of heat fluxes, the optimal design balances local temperatures to within 3 K. The analytical model is validated using computational simulations of the optimized heat sink. For a randomly-generated, non-uniform power distribution, device temperatures are balanced with a sample standard deviation below 2.5%, which is significantly better than a baseline design. When heat spreading is incorporated, the temperature increase is smaller but remains uniform, indicating that the hot spots can be mitigated.