I assume you are talking about a standard electric fan that you have in a room to circulate air?
If so, they don't have things that release poisonous fumes unless you consider the electrical components when they melt. The electronic components will release toxic fumes if they melt but so does the plastic.
The fan itself will not release any fumes under normal circumstances. However, new fans will often smell bad due to the plastics, glue and other materials they are made from. The smell is made worse by being sealed up in a plastic bag and put in a box for several months. The smell usually goes after a few days.
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Never use a fan on a bird at night because the bird's body temperature can drop very quickly and you kill the bird.
You can have a fan in the room with the bird during the day if it's really hot (above 35C), but do not have the fan blowing air over the entire cage, again because the birds lose body heat really quickly.
If the bird is hot during the day, use a plastic spray bottle with some water and spray some fine mist of water into the air above the cage. It will rain down on the bird and help cool it off. Some birds will also splash about in a shallow container of water and this helps them stay clean and cool off in hot weather.
Do not spray the birds down at night because they get cold and wet and die or get sick and need treatment.