You could use insulated panels or do a system with insulation but those would not give you the exact look you want. If you do this as an open air situation, I do not believe it will be too hot. I would suggest a roof that is very lightly colored on top. That will help.
I am interested in building a patio cover with a metal roof. I spoke with a contractor who said I would need insulation under the roof because it will absorb so much heat that it would be impossible to sit under it. But I have seen a lot of examples of patio covers with bare metal on the underside. I like the rustic look but don't want to do that if it will be too hot to use. I have included a couple of examples of what I'm talking about.
It will be open air and away from the house so I think that will work with a light color. I was thinking of Galvalume or silver color. Thanks for the help.