11+ years ago I built an incubator out of what looked like a cardboard box. My daughter who was 8 years old at the time wanted to hatch eggs for a science project.
It was a special box that we used to get at work with product in it that had to be kept refrigerated. It has a thin layer of foam built into it, and is lined with foil. (The foam is sort of like some of the foam cored poster boards)
I talked to my dad who is a tinkerer of all things electronic... and he had an old thermostat he gave me... actually 2. The first one had temperature swings that were to big, the second one was perfect. I hooked it up to a light socket and we were good to go. Oh, I forgot one important point, I thought it would make the heat more "gentle" is I put a heating pad in the bottom of the box, set on low, running continuously. (I used a 40 watt light, above the eggs, shielded with a mini lampshade.)
The box is double layer thick on the side walls, so I cut a rectangular "window" into the front, and put a piece of plexiglass between the two layers. I got a couple of old glass thermometers we were no longer using at work and used a shoelace to make a hygrometer. (I don't have that part any more.)
My daughter drew all over the outside of the box.
Her experiment: How tempertaure affects the hatching of eggs. We had the eggs divided into two groups. The one group was closer to the light and the other group was in the corner farthest from the light, with a thin sheet of foam separating the two groups. The goal was to keep one group at about 99 degrees and the other group 101 degrees. The warmer group hatched (on average) a day sooner than the cooler group. We had an excellent hatch rate. One dud, one dropped, I think the rest hatched.
My niece wants to hatch eggs now, so I dug out the incubator. It has not been treated well, so the box is a little warped, and the top doesn't close right anymore. I am presently getting it ready to give to my niece... and may post photos when I get it all straightened out.
Total cost of incubator? I think about $5. I have to go out now. Maybe I'll post photos tomorrow.
Maybe you could heat up your oven to about 150 or so and set it in there to soften it a little and then straighten it out that way worth a try if you do not get it too hot.