Plumage of penguins prevent the heat loss due to convection and help them to keep warm. Plumage work on land, but in the water where penguins spend quite a bit of their lives, they're not so valuable. On the land however, their plumage have a very valuable function in keeping them warm.
Penguin plumage aren't like the large flat plumage that flying birds have. They are short with an under–layer of fine woolly down. Penguin plumage are also very good at shedding water when the bird emerges from the sea. They overlap and give a good streamlined effect in the water and excellent wind–shedding abilities when they are on the land. When the climate gets very cold, penguins can puff their plumage out to trap more air for even better insulation. When it gets too hot (like as high as freezing point even!) they fluff their plumage out even more so that the trapped warm air can escape and enable the penguin to cool down.