Well, it seems you're serious; strange, but to each their own. You specifically keep mentioning the wall being cool. The wall's temperature has nothing to do with keeping the system cool - it's not going to act as a heatsink or anything. Cases are designed to allow a certain airflow pattern - typically cooler air front intake, warmer air rear exhaust. It's not the HS or fans that ultimately keep a system cool, it's the (smooth) airflow through the case as a whole.
I'm actually fairly curious as to how something like what you want to try would turn out. If you do it, take lots of pictures. Also, keep in mind that it will attract attention. Make sure it's firmly secured because you know people are going to poke and prod at it when they're over your house. Any never ever ever underestimate the curiosity or craftiness of felines.