Two directions of worry for this: heat buildup in the cookie tin overheating the lamp base, and hot metal of the cookie tin burning things around it. Neither one is that big of a deal, if you're careful.
The bulb sockets for table lamps and such are made to be operated in a "bulb-up" position, so that the heat is carried away better. They're rated for a given wattage of bulb based on that. So if you used a 150W socket, and you have a 40W bulb in the cookie tin, you're fine.
The bulb holders for ceiling lights are made for either horizontal or inverted lightbulbs - they don't shed heat as well, so they're rated higher. The Bakelite (looks like black plastic, but not) 2-bulb holder in my kitchen says "660W" on it. The fixture has a sticker inside saying to use 60W lamps maximum, so the socket is overrated for the fixture as a whole.
The ceramic holder I used for my water heater is rated for something silly like 1000W. I'm not even sure where to get screw-base lamps that hot.
As for the cookie tin getting too hot and setting fire to the litter in the coop, that's pretty unlikely. The can itself will get hot, but the whole surface is radiating heat, plus the waterer will be drawing heat off the top, cooling the tin, and then dumping heat into the cold coop.
Here's what you do to reassure yourself. Put a 40W bulb in the thing (or even a 60W, if you want) and plug it in somewhere in the house where you can monitor it, like the room where you are hanging out, or the bathroom or something. The air in the house is warmer than the coop, so this creates a "worst case" scenario for how hot it can get. Put it on a brick, or a tile floor, to prevent it from melting, say, the finish on the dining table. Check it after about half an hour, and again at about an hour. That should show the hottest it can get.
Safety First!! Check heat like you would a hot pan - feel with your hands from a distance and work in. You should be able to touch it at the corners (okay, it's round, but the top edge) and hold your hand there for a few seconds, at least. The middle may be too hot to hold your hand on it. If you smell hot paint, turn it off. If it's super hot, try rubbing a plastic spoon or yogurt cup on it for a "melt check." I doubt the metal will get hot enough to melt the plastic. If 60W gets too hot, go with a 40W. Some people here report using a 25W successfully.
If you really feel the need for an additional layer, screw (or pop-rivet) a cake pan large enough to hold the waterer base onto the lid of the cookie tin. That will make an air-gap like the "air bake" pans have to lower the heat conduction to the plastic.
