If birds survived when the rest of the dinosaurs did not, it may be partially because birds kept warm with feathers and when they lined the nest with feathers, the feathers would keep the eggs warmer. In addition, feathered nests protect baby birds from microbial infections and parasites.
One research write-up is here: https://doi.org/10.1002/ece3.6931. The study also tells a story of blue tit males placing colored feathers on the outside rim of their nests. Who knows why!