I got very familiar with this last summer
Environment
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our bodies transfer heat from our body to water on the surface of our skin, water that then evaporates, resulting in heat loss from our body
Not a great explanation. Sweat is obviously body temperature, so heat doesn’t move into it. Unless it turns into water vapor, which is a process that requires quite a lot of heat energy, cooling the remaining liquid or the surface.
I don't see anything wrong with this explanation? Sweat (or more pendantically the water in sweat) does evaporate and that effect does remove total heat from the body.
Yes. Your explanation is good.