We ran a number of different experiments measuring the temperature of containers of water as they cooled and we tried to describe the resulting data using Newton's Model of Cooling. All our results were the same. The constant k in the equation
A - T(i + i) = k (A - T(i))
is larger for high temperatures than it is for low temperatures. The same mechanism, modeled by Newton's Model of Cooling, cannot explain cooling at high temperatures and cooling at low temperatures.
At low temperatures cooling is a result of conduction but at high temperatures another mechanism becomes important. The molecules of water in our cooling cup are moving randomly, at different speeds and in different directions. Temperature is essentially a measure of their average speed. Individual molecules may be moving quite a bit faster than this average and some of them may be moving fast enough to escape from the cup of water. This is called evaporation and, although it occurs at any temperature, its effects are strongest at high temperatures. As the fastest molecules escape from the cup of water the average speed of the molecules remaining in the cup of water drops -- that is, the temperature -- drops. This effect is accentuated when a breeze is blowing across the surface of the water carrying the escaping molecules away.
The picture below shows one experimental set up with two temperature probes recording the temperature of the cooling cup of water in calm air and the temperature of the cooling cup of water in windy air simultaneously.
The graph below shows the data we collected in this experiment. Notice that not only does the water in windy air cool faster but that its temperature actually drops lower than the water in calm air.
Evaporative cooling is very useful. It is particularly effective in hot dry climates. In the southwestern states many homes are cooled by evaporative coolers or swamp coolers that use this principle as a cheap source of air conditioning.
There are several possible explanations for the difference between water cooling in calm air and water cooling in windy air.
One experiment you might do to get some idea of the importance of these two different mechanisms is to look at cold water warming up. What would be the effects of the first mechanism (an insulating layer) in this situation? What would be the effects of the second mechanism (evaporative cooling)? If you have a CBL try the experiment and interpret your results.