I am building a wooden case for my printer.
http://trilader.schroedingers-bit.net/blog/2013/11/17/a-better-case-for-my-3d-printer/
Your case looks quite nice, although complicated.
My route is actually replacing the side triangles with sheets of MDF. Cut to the right size, and carefully drilled, it directly replaces 6 rods, 12 nuts and washers. It also has vastly improved the stability of my printer.
Then you add on a back, top, and front. The sides have a cutout for the x axis. This will lose some heat, but if you really wanted to you could use longer threaded rods and move the sides to the outside.
Yes, my build plate is heated. The biggest concern is any plastic parts may soften. I am switching to 100% infill abs to combat this.
I think that with the sides slotted, it should get warm but not too hot, and prevent drafts.
I am still working on it, my previous iteration was laser cut, but I am moving to thicker wood.