I had to google it!
A pelmet (also called a "cornice board") is a framework placed above a window, used to conceal curtain fixtures. These can be used decoratively (to hide the curtain rod) and help insulate the window by preventing convection currents.
If I understand you correctly, are you referring to a hood of some sort?
If so, I would use either a good grade of oil based primer, then an oil based top coat. Or as many do, use marine paint. Check with local boat shops or supply shops.
I would go white inside to reflect any light.