I've accidentally had the litter container hide become a kindle box. I didn't add a wooden wall, just left the lid on, and let the lever portion act as a ramp in. Then one day there's fur in the back, and little wrigglers happily sleeping. Convenient thing about leaving the lid on, it was easier for kits to crawl back in if they got out.
Trouble was that after they weaned she treated it as litterbox. I suspect that it may have to do with existing smells, since there is little drainage for the kits' waste she decided that it was the bathroom.