The problem as it stands now is that she is experiencing something (“it is blowing cold air”) and your claims (“no it’s not”) run counter to that direct experience.
Place and leave a thermometer in front of it and give her the information that you are using to make your own claims.
You went through a process to learn that moving air feels colder than still air at the same temperature. It seems that perhaps she has not. Surfacing the ground truth of the air temperature may help the situation.
Full of enthusiasm I did this whole thing as they did in Veratasium [0]. Didn't impress anybody in my family. Although my son is getting there I think... Maybe I'm just too bad and lengthy at nerdsplaining.
Actually, I didn't put an ice cube on the metal, that is the trick. of course.
Place and leave a thermometer in front of it and give her the information that you are using to make your own claims.
You went through a process to learn that moving air feels colder than still air at the same temperature. It seems that perhaps she has not. Surfacing the ground truth of the air temperature may help the situation.