I'd wait for other's to respond as I don't actually know for sure, but I have a popcorn maker that uses hot air. I don't use it in the same room (as any cooking or heat related thing beside the heaters, I keep it out of the bird room/lounge).
Although I use it I don't know the mechanics of why it shouldn't be safe. As long as you don't leave it unattended and food can't get trapped in it, it shouldn't burn; and although I don't know if PTFE was used in any parts of it, I don't believe the device should get hot enough for that to be an issue (unless you leave it unattended for a significant amount of time), the reason I don't think the device should get hot enough is because if your device is like mine it probably has a lot of plastic in/around it, too much heat would cause the device problems. Not to say the device can't get hot enough but again if you attend the machine then the popcorn will be ready long before melting plastic is an issue (another problem for birds there, plastic fumes).
Please listen to other people too, I also want to know if my thinking is wrong. I also don't want to cause unnecessary harm to my bird.