I used to do that, (Sprinkle or mist eggs under a hen) my DH convinced me I didn't need to. The eggs still hatch just fine, but the hens are less annoyed in the process. Hens don't sweat, but their underbodies still transmit the correct amount of moisture to the eggs. Feel the skin on the underside of a broody, it feels very warm and slightly damp. Not wet, but you can feel the humidity.
The hen just needs a safe, protected space to brood, free access to food and water for her daily nest breaks, and the nest should not be too far off the ground. That way when the chicks hatch, and she leads them out of the nest, (usually the day after they all finish hatching, and have had time to fluff up and become active) they will be able to leave the nest without a long drop. I've tried to put mine in nests on the floor of the coop, but right now I have 3 broodies, one in a floor nest, two up higher.