How much cooling is my mist maker humidifier causing?
What you're asking about is the latent heat of vaporization. 

It is 970 real BTUs per pound of water, or 2260 joules per gram.   A joule is a watt-second.  A BTU raises one pound of water one degree F.

That means if you have an ugly bag of liquid water, 1 pound, and it is 112F temperature, and you inject 100 BTU, it is now 212F.  If you inject another 970 BTU, it is still 212F but is now vapor.  If you inject 30 more BTU to make it an even thousand, it is now 242F.  The 970 BTU was eaten by the phase change.   Yes, you can use this to air-condition, but it works better with freon, propane, etc. 

There's no free lunch.  That energy has to come from somewhere.

A gallon of water is 3785 grams (also 3785 ml, by wild coincidence, not). It will take 8.5 million joules or 2400 watt-hours, or 8200 real BTU,  to evaporate it.   If the humidifier avoids paying it (e.g. By misting), it is stolen from the air, cooling the air.  

By "real BTU" I mean BTU is a timeless unit.  Remember when a furnace talks about BTU, that is slang. It actually means BTU/hr.