Here's a drawing that lets you see how the air enters and exits the box. They actually do so right next to each other just inside the partially opened window in this design. Because heat rises, as long as the warm exhaust is on top, the bottom will always pull in cooler air from the bottom. For that reason, you have to insulate and caulk the box well so you are sucking in cold outside air.
There's no reason you couldn't cut one low hole right in the side of the coop (intake) and one high hole (heat exhaust) if you don't have a convenient window, I just don't want to have the panel on the coop permanently. I will do that some day when I install one on my home. That would also save you having to build the intake chamber.
So yes, as you can see from the diagram, you are heating coop air. My little model was just a proof of concept and it is only heating outside air. But I will take that window (it's just a freebie doublepane vinyl clad window), build a 2/6 or so box, insulate the back and sides of the box, put my metal collector inside the box (with a 2 or so inch gap behind the collector for air intake), and then build a little divided chamber that sticks inside the partially opened window (bottom pulls in cold air via thermosyphon from the hot air that is exhausting just above).
By the way, I saw a youtube of some energy company that took and existing window in their shop, boxed it in w/ a metal panel, and put a fan on it. Quite frankly, I'm not seeing how that produces a radical benefit (except that it insulates the window, I suppose). The energy of the sun is already going in that window -- the collector doesn't make any more. What you need to do is get more windows. By putting the collector on the wall (or below the window as I plan to do) you are, in effect, INCREASING your window area and, hence, your passive energy absorption. Cover up an existing window w/ a box and you'd lose light and as I understand it, you don't want to cheat your girls out of light.
And one more p.s. This is our first year with chickens. We have 16 and yesterday we got 10 eggs -- new day total. Whoo Hoo. But I tried to carry them all at once and broke two. Boo Hoo.
I agree...fun thread. I'll post pics when I get my box done -- maybe this weekend (famous last words).