I think I'd try and find an old electic brooder or incubator with a wafer thermostat. You might get one very cheap if the heating element is out on it. I have the feeling you are going to have a hard time keeping others in the narrow range you want. If I found a wafer thermostat, I'd get a replacement wafer for it if possible, some feed stores still keep them. You might loose all your eggs you are hatching if you try to economize too much on a thermostat.
I looked at the link darkmatter gave and the thermostat there is of the type the wafer thermostat is, so that might work if you want to go to all the work to make the disks, which you could buy for $12 maybe less. The wafer disks work with a micro switch when they expand enough the switch turns the power off, they cool down a little and it goes back on. My thoughts for most thermostats a swing of 6 degrees isn't a problem, you want water at 130 degrees and it gets to 136, no big deal. You want your incubator at 101 degrees and it gets to 107, you've got problems.
One thing that did come to mind that is regulated at temperatures closer to an incubator is a yogurt maker. I think they keep the yogurt between 110 and 120 degrees. Maybe that thermostat could be regulated down a little. I guess if you are experimenting and just putting in say 6 eggs it might be worth a try, you wouldn't be out much.