I've reached the end of my expertise in this area, but I am sure that there will be others that will contribute.
Story time: When I moved to Buffalo. NY, at the ripe old age of 23, I lived in a two room efficiency apartment. There was this furnace register thingy in the corner of the apartment and when turned up all the way - I still froze. So I put a fan on top of it, in the hopes that it wouls circulate and warm me up a bit. Incredibly, it did. Not only that, I was actually able to turn it down. The point is that circulating the air causes a more even distribution and should be able to knock the temperature back to tolerable levels, especially if it isn't totally sealed off. I realize that there are several variables interacting and it cannot be predicted as to its final effects, but I think it would be worth a try.