I have cut out most scented products from my home because of my birds needs and because I het scent-related migraines. Even so, a natural pump room spray most likely killed a young Gouldian finch of mine. Migraines give a person a great awareness of how much fragrance is used in products that maybe don't need it. Even regular laundry detergent is pretty stinky. I go with "fragrance-free" or unscented or "free and clear" products as much as I can.
I think it's better to not use air fresheners at all, or any cleaner that smells strongly. Turn on fans, open windows, etc when cooking or cleaning. Also, many cleaners and room sprays contain Febreeze which is super toxic. I've become aware of this because it gives me a terrible migraine if I smell it at all. I use plain diluted bleach or vinegar to clean many things. BUT these also are toxic in high concentrations and must be ventilated.
I got rid of my nonstick cookware because burnt or overheated PTFE kills birds and hurts people's lungs. I have well-seasoned cast iron that I use for frying. I do use cooking spray on it but with the oven fan on. Unfortunately, I'm in a small apartment, so if I burn something while cooking, I have to run to open windows. I've been known to move birdcages into the bathroom with the fan running if I burn something or notice a strong product smell.
It's more important to get fresh air than to worry about temperature. If you have an accident, get your windows open and a fan going even if it's cold out. A bit of a draft isn't going to kill a healthy bird. Smoke or chemicals will.