This paper presents a heuristic optimization method for cooling channels with internal repeated-rib roughness. The method rapidly explores a design space to simultaneously optimize two geometric parameters, channel length, and rib roughness ratio. For a rapid and accurate optimization, the method combines a heuristic optimization technique, simulated annealing (SA), and numerically derived closed-form models of heat transfer and pressure drop. It is shown that approximately 1 million designs are evaluated within 6 s, resulting in optimal designs having minimal thermal resistance for given pressure thresholds. Closed-form correlations for developing and fully developed flow are derived by evaluating discrete design points using a finite volume model (FVM). The derived correlations predict the channel properties with acceptable ranges of mean absolute error (<5% for Nusselt number and < 15% for pressure drop) against the FVM. Optimal channel designs exhibit up to about 12 times greater performance factor compared to smooth channels, supporting the efficacy of optimization. The introduced method demonstrates the potential of rapid numerical optimization method in designing heat transfer devices with complex geometries.