grob : Shirley Temple (really??), driving a .....???

[Otto Puzzell]

The girl in the picture looks more like her, but except in this picture from that photoshoot, where she wears special glasses for skeet shooting, I can find no picture of Carole with glasses. And this girl surely needed her glasses.
Also, Eisenstaedt, as one of Life main photographers, photographed a lot of people.

Also, too, if "Shirley Temple's hot rod" seems a phony identification, I found "Alfred Eisenstaedt 1938" on Facebook and couldn't trace this to a source. So it's just more logical, but that's all.

Shirley Temple turned 10 in 1938. Here is a picture of her at 26 - looks nothing like the picture girl.

[grobmotorix]

You must be right. Still we do not know the car...