Double wall cooling is a very effective technique for increasing heat transfer in hot gas path components utilizing a narrow channel near the surface of the component. Multiple techniques exist to increase the heat transfer within the narrow channel, including the use of impingement jets, turbulators and microchannels. A preliminary study has been performed using computational fluid dynamics (CFD) to determine the heat transfer benefits of double wall cooling technology when compared to a smooth wall square channel and a ribbed wall square channel. Conjugate CFD simulations of flow through an aluminum channel were performed to include the effects of conduction through the solid and convection within the main channel. The design for the preliminary study consists of a square main channel and a narrow impingement channel connected by a series of holes creating impingement jets on the outer surface of the impingement channel. The study examines multiple parameters to increase heat transfer without increasing the pumping power required. The parameters studied include diameter of impingement jets, jet-to-jet spacing, number of impingement jets, and jet-to-wall spacing. Results show that the impingement channel height-to-diameter ratio has a strong impact on heat transfer effectiveness. This study also provides a new optimization methodology for improving cooling designs with specific targets.