Henry,
Metal is by far going to be the best material that you can use in this application, but isn't very practical for everyone. The next step would be to build one out of wood. The wood, even though it is still flammable and combustible, will take much more heat before it would ignite.
Henry, if you can build a quick wood box out of 1"x pine, and be sure that the heat source is a couple inches away, you should be fine. Or if you have a piece of tile backerboard (concrete board) that you can place between the wood and heat source, you will be fine.
Cardboard as you now know, will go up quickly, and plastic will start to melt and produce toxic gasses if the heat source is allowed to get too close. If you have a means to keep the heat source several inches away from a plastic tote, and can check on it often, you can probly get away with it.
This is one thing that has been scaring me really bad the last few days with folks displaying the pictures of the incubators made out os a styrofoam cooler. The same thing is going to happen there. Styrofoam will melt quickly if the bulb is too close to it and then start the fire.
Folks need to watch this very close. Most of you have these types of set-ups and they are in your own home. So, when it happens, you don't just lose a barn of chickens, you lose your home, your memories, and possibly your family.
Please learn from Henry tonight. Take a good look at how you have things set up, and make sure you aren't next.