To obtain better fluid mixing and higher heat transfer in the low Reynolds number regime, various wavy fins are employed in heat sinks (heat exchangers) for electronic cooling applications. However, it was reported in previous works that in the low Reynolds number regime there are no remarkable differences in the thermal performance of a straight-plate and a wavy-wall channel. In this study, the constructal theory is applied to optimize the geometry of wavy-wall channels of an electronic heat sink, where the objective is to minimize the global thermal resistance. The domain has three degrees of freedom: The interplate-spacing (S), the wavelength ratio (λ1/λ2), and the amplitude ratio (a1/a2). The two times minimized global thermal resistance indicates that the thermal–hydraulic performance of the wavy channels is unaffected by the amplitude ratio, while the wavelength ratio and interplate separation have strong impacts on the overall performance. In addition, the thermal performances at four Reynolds numbers are evaluated, and it is found that the constructal-wavy channels can exhibit much better thermal performance in the low Reynolds number regime.