[potatoz2]

I'm not sure I follow what you're saying. A blind outside is just like a curtain, except that to whatever extent it heated up it is heating up directly outside (via radiation or convection). A curtain that's hot in the insulated enveloppe is strictly worse, everything else being equal (color, etc.)

The radiation of the sun has to go somewhere. More of it will be reflected back by shutters, and whatever is absorbed can more readily be dissipated outside than inside.