If the broody hen doesn't have enough room to really distance herself from the others I would really recommend segregating them somehow. There are just so many complications that can come up otherwise. Squabbles over nest boxes, ending up in the wrong nest box, possible issues with the chicks...
Misting systems work like a swamp cooler, through evaporation. Evaporation of the mist actually makes the air cooler - as water changes from a liquid to a gas, it drops in temperature. This is why these systems are useful mainly in low humidity conditions, which have more evaporation.