Spraying of water in an incubator creates local cooling, as the eggs that are close to the sprayer will lose more heat to facilitate the evaporation then the eggs further away.
To avoid this cooling effect, sometimes water is warmed up before it is sprayed into the machine. However, this will not influence the cooling effect as much as we sometimes think.
First of all, the energy needed for evaporation is much more then the energy needed for warming up water. It costs 1 calorie (4,2 Joule) to warm up a gram of water with 1oC, where evaporation of water costs 540 calories per gram. So even if it would have an effect, the difference between warming and evaporation is enormous, so warming up the water 20 or 30 degrees will not have a big influence. But besides that, the amount of energy that evaporation costs is not dependend on the temperature of the water, it remains 540 calories per gram.
A good way to demonstrate is to put warm or cold water in a sprayer that is used for instance for plants, and spray on your arm from a distance. What you will feel is a cooling effect, regardless of the initial temperature of the water