How hot does a dark color steel roof get

If you see a color it is because that color is not absorbed by the object and it is reflected.

Black has no color and absorbs all light

White has every color and reflects all light

Reflective (shiny) rejects all light

A major component of heat is infrared light. Black absorbs it all and mirrors reflect most all of it. Now heat will build up in any structure that is not well ventilated and is tightly enclosed, thus all cars sitting in the sun heat up. But alot of that heat comes from the glass allowing all IR in and not having ventilation. Heat will build up next to a metal roof with all colors because of the thermal coefficient of metal and its ability to transfer heat from one side to the other. Anyone that owns a vehicle painted black knows it is hotter than one painted white but they both are hot when you come out in the afternoon to go home. A simple experiment is to put a thermometer in the trunk of a black car and then place the same thermometer in the truck of a white car. You will see a difference but both will be hotter than the outside temp because of thermal transfer.

In summary ventilation is the most important factor in design but a dark colored roof will get hotter than a light colored roof. A fact based on simple physics.

FYI - A friend of mine bought a place with a painted roof on the barn (40x60). It was built in the mid 80s, 4/12 pitch. We crawled up there to chase down an electrical problem with an outdoor light, There wasn't a speck of paint on it, go'na cost him 2 grand to replace it.