Although a tin roof will get hot either painted or not, white would however reflect some of the heat, yet only minor.
Inside, when i built mine, i lined it with insulation and clad the walls with simple ply, which i left natural, it all worked well.
My observatory was a little different, the roof did not roll away, but the entire building moves out of the way and exposes the rig.
A bit different i know, but it worked well for me.
I also put a fly over the roof with a cavity which would reduce the heat enormously as the roof was shaded and the air would flow through the cavity.
Leon