If it has teflon, I wouldn't use it. If it gets over a certain temperature it can kill your bird. These things aren't just harmful, they are deadly and the death caused by teflon (in particular) is a horrific death and can happen quickly.
My motto is, if in doubt, don't use it. I often email companies if I'm not sure of something in them and ask.
Some people will tell you closing the door is OK, some will tell you its not. I just don't take the chance. Its not something I can undo.
Hope that helps.