I’m wearing too many layers and it’s so hot. Could you fan me?
Because the hiragana ends with an う sound, you know this word is a verb. The kanji itself means folding fan and since you don't "to folding fan" something, this word means to fan instead.
Imagine yourself trying to fan yourself with an 青 (あお) fan. For some reason blue fans feel cooler. Maybe it's because they're the color of ice/water?