I have parrots and they die a really horrible death really, really easily when non-stick pots and pans (Teflon) is over heated. Sometimes heat lamp bulbs are coated in the stuff, too. It's even in clothing now.
I would guess that the inside of a self-cleaning oven might be coated with something that would be similar to Teflon.
It doesn't take too high a temperature for the chemicals in a non-stick coating to start off gassing, something like as low as 500F. The more used and worn the pot is, the lower the temperature it starts to off gass, sometimes as low as just over 400F.
The usual scenario for bird deaths is that a pot was left on the burner and forgotten, but it doesn't take much for the temperature to reach 500F when frying. It is a really horrible death. I've had vets describe their experience of trying desperately to save birds.
Bird people just never use non-stick cookware. The manufacturers of the chemicals have not been exactly forthright with the risks.
http://www.ewg.org/research/canaries-kitchen/teflon-offgas-studies
It gets into people, too, and causes all kinds of problems with compromised people like newborns.
Birds and reptiles are very similar although their respiratory system is not, which may be why birds are so easily killed.
If I use the self-cleaning feature (almost never) my birds (and now chameleons) will be out of the house for at least a day and the house will have windows and doors open and fans running for a day.
Teflon is a surprisingly toxic chemical.