I have made a number of beds for the cats. This is a fairly quick and simple project. You need a table saw or a router with a 1/4 inch cutter that will cut to 3/8 inch depth.
I noticed that the cats liked cardboard and corrugated boxes and box lids of a certain size. This is the size that I made the box out of wood. The sides are a little higher than the preferred lids but my wife makes Polar Fleece “puffs” to fill the bottom and the cats seem to like them.
The first box lid that the cats liked was the tray that came in the citrus fruit from Florida. This tray had doubled sides and seemed to be a particular favorite of the cats and so became the model for size and proportion. This one is 16 by 10 1/2 inside. This makes the length 17 1/2 and the width 12 inches.
The basic idea is simple. Four sides and a bottom. The bottom is fairly fixed. It is 1/4 inch plywood. The sides give lots of options.
The first option is the choice of material. Pine, oak, and cedar are good choices. Pine is inexpensive and easy to find and work with. Oak is pricey and pretty. Oak looks good indoors and ages gracefully outdoors. Cedar is rot resistant and can be pretty. Not too expensive but cedar splits easily if the corner screws are over tightened. The height can by the 5 1/2 inch width of 1 by 6 or the 7 1/2 inch width of 1 by 8. And a couple that we have are from 1 by 4. Of course the 1 by is 3/4 inch thick.
The box construction is straight-forward. A rectangle with the long sides (length) overlapping the ends (width). The bottom is set in a groove around the bottom. The groove is 3/8 inch deep in the 3/4 inch thick sides. Cut the plywood about 5/8 inch wider than the width and 7/8 inch shorter than the length.
For the box above, this would be 2 pieces 17 1/2 inches and 2 pieces 10 1/2 inches. The bottom is 16 5/8 by 11 1/8.
NOTE: Follow all general and specific safety instructions for the tools you use.
Cut the side and ends to length. Set the saw blade (or router cutter) height to 3/8 inch above the table and remove the splitter so that you can dado a grove. Be very careful if this leaves the blade unguarded. Check the height with a piece of scrap and adjust it until it is just the right height. If you are using a router, you and your router may be happier and your cutter may last longer if you make several passes increasing the depth until the final depth is reached.
Set the fence so the close edge of the blade is 3/8 from the fence. Carefully make a pass through each piece. If you are using a 1/8 inch saw blade go on to the next step. If you are using a 1/4 inch router cutter, skip the next step.
Reset the fence so that the far edge of the blade is 5/8 from the fence and just a scosch more. Test it with the scrap. Try the plywood bottom for fit in the slot. If it is loose, move the fence closer. If tight, move the fence a bit farther way. When adjusted, make sure that you hold the previously cut edge toward the fence and carefully make a pass through each piece. When you have cut both sides, you may need to clean out the bottom of the groove with a 1/4 inch chisel.
You now have a 1/4 inch groove in all 4 pieces.
Trial fit the sides and ends against the plywood. The plywood should fully close the bottom. The sides should mate up tightly against ends.
Drill and countersink a hole in each side 1 1/4 inch from the bottom and another 1 inch from the top. IMPORTANT: Assemble with brass screws. Steel screws and galvanized screws will leave stains on the wood. Brass screws will turn a pretty verdigris if they do anything.
Line with a blanket made from Polar Fleece. Make sure that there are several thicknesses and that the ends and sides of the liner extend beyond the wooden sides.