You have misconception about boiling point of water. In order for water to be in gas form it doesn’t have to be over boiling point of water. Boiling point of water is the point where water molecules overcome liquid-phase intermolecular forces so it turns into steam.
You can also overcome those forces with kinetic energy. It’s called evaporation. And it occurs at the surface of the liquid. Rate of evaporation depends on temperature and relative humidity of surrounding air and also movement of the air.
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