Never EVER happens. Parallel evolution does not work that way.
Superficial appearances DO converge, microstructures NEVER converge. Instead, the problem is invariably solved a different way the second time. The resemblance between fish, whales, and ichthysaurs is entire superficial (except for their common vertebrate ancestry, of course).
Example: Keeping warm:
Solution 1. Hair
Solution 2. Feathers
Non-flying birds with much down, appear to be covered with hair, and it has the same function as mammalian hair, but the structure is completely different.
Feathers evolved exactly ONCE.
The question is: Did feathers evolve in dinosaurs or in their archosaur ancestors and were then lost in all lines except the one leading to birds? Sounds pretty unlikely. I vote for birds from theropod dinosaurs.
David F Mayer