Tom i think metal roofs wouldn t show as big a temperature difference because they reflect a lot of the solar radiation.
Temperature of a steel roof in the sun.
Other roofing materials capture and retain the sun s heat.
Second metal roofs lose any gained heat very quickly to the sky when the sun sets or goes behind a cloud or even when a slight breeze blows.
Degrees fahrenheit on a sunny 90 degree day.
Third many metal roofs especially the shingle shake and tile look ones have an integral airspace between the metal and the roof deck.
If people can touch it easily the temperature is a concern.
If the building is located in hammerfest norway the metal might get warm to the touch.
The iron isn t going to melt.
If it s on the sun facing side in las vegas you may find it gets hot enough to cause burns.
Still the shine of bright white on a roof is imposing and can take away from the overall aesthetic of the house.
White shingles keep vented attics more than 15 degrees cooler than black shingles and a reflective metal roof would do more than that.
Here s the kind of temperatures you can expect your roof to reach this summer depending on its surface.
A definitive answer is not possible.
Imho i would still hedge my bets a little and suggest 180 degrees f.
If it s out of reach don t worry about it.
A more obtainable maximum temperature for a properly designed solar collector is 150 degrees f.