Hot glue or tape your box closed securely.
Use a ruler to trace straight lines 2-3" from each edge of each of the 4 vertical sides of the box.
Cut along your marked lines with a box cutter to make a squared opening in each of the four vertical sides. Cut a piece of fleece that measures the dimensions of the bottom of your box PLUS an extra 4" on each side. (Ex: For an 18x24" box, you’d cut a piece of fleece that measured 26x32").
Cut a 4" slit into each of the 4 corners of the fleece, toward the center.
Cut two small holes about two-thirds of the way up your box, one on each side of the corner.
Feed the two slits of each corner of the fleece through the holes, and tie them into a secure knot.
Cover the bottom of the box with another piece of fleece, in case your kitty would rather hang out there.