It is pretty well accepted that lighter colors reflect heat, but then I haven't done any real testing.
I have to say that colors of shoes really do not seem to make any difference to me. I hike in all kinds of weather and choose my shoes for the requirements of the trip, without taking color into consideration at all. Doesn't seem to matter. When it is hot the lightweight mesh shoes work just fine whatever the color... although I don't have black ones. When it is hot out, I am sweating at the top of my body, and I am not even thinking about my feet.
However, shirts do make a difference. If they didn't get so dirty, I would wear white eco-mesh shirts in the heat of the desert.