If the fan is running because ambient temperature is hot, then I would not worry about it.
Drafts are cold air drawn indoors by a difference in temperature. Chilly air can move heat away from the body faster than it is generated so it can cause dangerous heat loss in small animals, especially birds that are very young, molting, or missing feathers.
A healthy, well-fed bird is at less risk than a sick or malnourished bird because they are able to burn excess energy for warmth. But even a healthy fully feather bird can die eventually, if it is kept in a cold drafty environment, just as you can die or become ill from being exposed to the elements for too long. This is especially true for tropical species that lack cold tolerance.
Deaths tend to happen at night when ambient temperatures drop to the lowest point.
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So long story short, check for drafts in winter. A cool breeze in summer time is perfectly fine.