Insulation, Radiant and Vapor Barriers - how do I insulate this windowbox?

my breezeway is covered so rain isn't an issue but obviously i want to keep the cold from getting in this new box.

right now i was thinking just cut another piece of wood and then sandwich in some spray foam between them and then foam around the perimeter once the outside wood is screwed on.

Or go buy some styrofoam for the sandwich part and just foam outside?

http://i371.photobucket.com/albums/oo155/luckydriver/crown/IMG_3074.jpg

http://i371.photobucket.com/albums/oo155/luckydriver/crown/IMG_3073.jpg

I would just use plain old fiberglass insulation. The foam idea won't work because the small cans of foam won't cure right if they are put on too thick. The ridged foam insulation is tough to get a tight seal around the edges and it cost a lot more than a roll and you'd have a lot of extra left over.

when i think fiberglass i think of the pink stuff thats 1ft thick in my attic. Is there another kind you are referring to? I think that's maybe 2 inches of space (i havent measured) so am unsure how that can be compressed plus i need an additional piece of wood on the outside yet. or does it come 'skinny'? There probalby will be only an inch or so of empty space between the 2 pieces of wood. Also i just need the tiny piece for that space so would be buying anything and dont want to buy a huge roll just for a little piece.

Just use 1 sheet of: Dow at Lowe's: 1" x 8' x 4' R-6.5 Polyisocyanurate Rigid Foam Insulation (http://www.lowes.com/lowes/lkn?action=productDetail&productId=42864-236-263065&lpage=none) or the 1/2", don't get the white as it will let moisture through. Cut to fit, caulk each piece, add plywood last, caulk. 2pcs. = R- 13
Be safe, Gary