The problem there is that red is a close second in photo-reactivity to black, so it's nearly as hot. Red also has a tendency to oxidize quickly, requiring frequent repainting, which is one of the reasons most railroads stopped using it in the 1960.

CD

IC also used red on the cab roof.

I don’t think red was used in consideration of heat transfer. While light colors reflect heat and dark colors absorb it, the surface texture plays a larger role. The difference between black and red would be minimal if both were similar in the range from shiny to dull.

Another consideration is whether there is more heat being generated by the boiler inside of the cab compared to what is being absorbed from the sun from outside the cab. A mirror stainless steel would be an excellent reflector of the sun’s heat. But it would be a poor emitter of the cab interior heat. So if there were more heat being generated by the boiler within the cab than what is coming from the sun, then a mirror stainless steel finish on the roof would effectively insulate the cab from heat loss and make it hotter while flat black would make it cooler.

One thing's for sure - the tender decks on the Southern passenger locos were indeed a rather bright red. There is movie footage of a PS-4 nose first in the turntable pit at Spencer, ca. 1950, that clearly shows this. The cab roof, however, is black. Perhaps the CNO&TP passenger engines had red cab roofs, but power on the other division did not have this feature. I recall asking the late Shelby Lowe about this many years ago, and he said the cab roofs were always black as he recalled. All of the color steam era photos I have seen of Southern power show black cab roofs.

One thing that was unusual with regard to passenger power was the Ts 4-8-2 #1454, which received the standard Southern passenger striping and lettering, but got painted black where the green was normally applied. I wanna say it was late 1940's. I have prints from the photos that Shelby Lowe took at North Avenue Roundhouse with the black engine wiper posing on the running board that Shelby used colorful language to describe how that blankety-blank insisted on posing and not getting out of the picture. As a chief clerk in Atlanta, Shelby was able to get the roundhouse foreman to pose the locomotive for him out of the roundhouse. On a related note, Shelby also managed to get 1380, the streamlined PS-4 sent to Atlanta as power on a passenger train in June, 1947 so that he and Dick Sharpless could get photos of the locomotive after it was released from captivity on the Tennesseean between Monroe and Washington. The got it at Lula, Georgia on train 39.

Meeting Shelby Lowe and getting to spend the day with him several years ago was a real treat. I wish he was still around.

Mike
Look Ahead, Look South

I had heard (long ago) that the tender decks were only red on locomotives equipped with stokers...so the crews that coaled the engines would know and be aware of the presence of stoker equipment in the tender.

I want to agree with the black cab roof. I have seen some evidence of that too.

And if you have studied the subject long enough you will find many exceptions to every rule. As much as we might want to think they followed strict standards it was obvious that shops made exceptions all the time. And I guess we all know that paint schemes and other details varied widely from division to division (do we still remember that)?