Jennifer Lawrence and David Letterman Get Cozy Under a Blanket

TV Watch

By Tim Nudd

11/21/2013 at 10:05 AM EST

David Letterman and Jennifer Lawrence

Jeffrey R. Staab/CB

Jennifer Lawrence was as friendly as ever on CBS's Late Show with David Letterman on Wednesday, but she wasn't particularly warm – until she was handed a big pink blanket to fight off the chill.

And soon, she was joined under the comforter by the host himself, who then joked that he wanted the audience to leave immediately.

"God, can it be any colder? … It feels like all the windows are open or something," the Oscar winner, 23, said at the beginning of the interview. "Do you ever get so cold that you start sweating? Is that just a gross problem I have?"

Letterman, 66, got her the blanket, then sat down beside her, and they disappeared under it.

"Goodnight, everybody!" Letterman called out. "Oh, I wish they'd go away. I wish they'd go away, don't you? They can't see us now. Go away, everybody!"

"Go away!" Lawrence shouted with a laugh.

"I wonder if they're gone. Are they gone? I hope they're gone," said Letterman.

"I don't know if they're gone, but the rumors are going to start," Lawrence added.

If she hadn't been careful, Lawrence might have actually fallen asleep, as she admitted to being exhausted while promoting her two new movies, The Hunger Games: Catching Fire and American Hustle.

"I'm so tired!" she said later in the interview, as she rested her head on the blanket.