The female usually does the incubating because she has temporarily a bare patch of skin on her underside called a brood patch. The brood patch is created when the female loses feathers on her belly. The area of skin exposed is thick and has many blood vessels. This allows the heat from her body to be transferred to the eggs. The normal development of the eggs can be harmed if they get too hot.
Different species have different ways of protecting eggs from overheating.
Some birds stand over the eggs to provide shade. Ducks cover the eggs with feathers to provide shade when they must leave the nest. Shorebirds like the killdeer soak their feathers in water and return to sit on the eggs. The wet feathers help cool the eggs and keep them at the proper temperature. Still others like the house wren simply adjust the amount of time they sit on the eggs according to the temperature of the air.