Pierre the Penguin: A True Story by Jean Marzollo, illustrated by Laura Regan

From chapters.ca:
When Pierre, an African penguin living at the California Academy of Sciences, begins to lose his feathers, the zoo staff is at a loss as to what to do. The lack of feathers causes Pierre to lose warmth, making him afraid to swim in the zoo pool. And the other penguins start to shy away, giving Pierre the "cold" shoulder. Unfortunately, heaters and medications fail to correct the situation. But one rainy day, inspiration strikes a biologist named Pam. While walking her dog in the rain, Pam notes that her pet wears a raincoat. Could a "raincoat," or wet suit, help Pierre? A tiny neoprene wet suit is designed especially for Pierre. But will it work?
Told in rhyme by noted I SPY author Jean Marzollo, this true story of veterinary ingenuity charmingly comes to life.