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My '07 Z51 A6 coupe had no oil cooler, I retrofitted the Z06 oil cooler and lines to the car. I did buy another Z06 shroud so I could precut it and it had the oil cooler bolt holes and oil line holes for easy alignment.
Hope this helps. BTW it certainly helps with the oil temps, engine coolant and oil temps always seem to be within 10+/- of each other under normal conditions..
All manual trans '05 to '07 Z51 have the engine oil cooler in the radiator. Auto trans Z51 does not. The manual trans Z51 also has trans cooler. In '08 there is a seperate cooler in front of the radiator.