Thunderbirds can be found in the Iron biome sitting on their nests. They watch the player, turning their heads towards them. If the player gets close (about 2 fork tiles) the bird will charge up, making electric sound and charging animation. If the player gets too close (about one fork tile) the bird will shoot out three lightnings around him at random, likely hitting the player with at least one.
They can be chased down and killed after they release their charge, since it takes them about minute and a half (further confirmation required) before they can strike again.