Hi David,
I use an aluminum radiator with a tank in the rightmost header for my C6 automatic. I've run up to four track sessions in a day without any signs of heating in the automatic. Of course, a lot depends on the converter's stall speed, mods to the auto itself etc...
Having said that, the fittings look a lot smaller to me for the auto, implying a lesser flowrate. The auto's cooling lines are -6AN where the engine
oil cooler is -10AN, a really big difference. The smaller fittings might also imply a potential restriction in the engine
oil circuit.
My engine
oil cooler is not located in front of the radiator - it is just below it so it doesn't seem to influence the engine cooling at all.
The above speculations are intended to be helpful
Tom