Heat is energy, movement is energy. The water hits the wall and transfers energy to the walk, this is the kinetic energy that pushes the drop of water away. In that moment of interaction, the heat in the water can also be transferred to the wall, so you have a cooler drop of water, depending on the heat transference.
Water gets heated from a fire.
Water comes out of the showerhead and immediately loses a lot of heat because the tiny droplets adjust to the ambient temperature.
If the tiny droplets hit the surface of something, it will cool even faster because water touching an object will cool much faster than just touching air.
[Surface area to volume ratio](https://en.m.wikipedia.org/wiki/Surface-area-to-volume_ratio)
Anything with a smaller surface area to volume ratio will cool much slower.
This means, with droplets in particular, the smaller the droplet, the faster it will cool down.
It does however, change for different shapes because the ratio changes. You could have the same volume in 2 shapes, a sphere, and a very thin disk, but the sphere will cool slower, because the thin disk (like a dinner plate) has more surface area compared to its volume in comparison to a sphere
When a water droplet hits an object it “splatters” or turns into a bunch of smaller droplets. These droplets have a very large surface area to volume ratio compared to a larger droplet, to the point the ambient temperature of the area and surrounding materials cools it incredibly quick.
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