As you can see, I gave up ever having my own access to this storage box. And laid down a fuzzy thermal pad, so that Cinnamon would be cozy in her lair.
Except that it is a constant hassle, having to straighten it out. In order to enter the Cinna-cave, she has to leap in from the nearby loft ladder. (Spectacular coordination required for that, by the way. I watch with fascination every time she does it.)
But when she leaps in, invariably she rucks up the fleece pad as she lands. It is constantly being pushed up against the back.
Whenever I pass by and she is not in the Cinna-cave, I straighten out the pad. At least once a day. When she IS in there, I reach in and give her a few skritches.
About half the time she gets annoyed and bites me (but not hard). The other half she curls up and squeaks with joy. Hard to say with this cat sometimes.
I keep threatening to get a wireless webcam and train it on her little cave. Cinna-cam! 20 hours a day of a cat sleeping in the dark. FAAAscinating!