And why just cover it, when you could put a glass lid over everything and leave it out in the sun?
I've made a wooden box that is 20" x 24" and 9" high. The walls are scrap pieces of 2x10, and the bottom is a sheet of 1/4" plywood. It's spray painted black on the inside and near the top of the walls I've milled a slot so I can slide a glass cover over it (I got a scrap of tempered glass from the local glass shop). It gets plenty hot inside the box when it is sitting out in the sun. It also helps to have some jet black bowls, cups, and saucers (from the dollar store) to put the food on.
My next project is to put a mirrored lid on it so that twice the sun's rays hit the inside of the box.