At the end of the piece, Satch says, "Now we're get'n warm."
Here's a bit of Anthony Lane's piece on Grace Kelly in the New Yorker:
It is customary to denigrate “High Society” by comparing it with its parent, “The Philadelphia Story,” but I knew the child first, when I was a child, too, and nothing can undo the movies that we are led to in our youth, or the skein of impressions that they leave. I remember my mother explaining to me, drawing on who knows what store of apocrypha, that Prince Rainier had watched the scene of his wife-to-be, droopy with drink, being lugged through the moonlight in Sinatra’s arms, both of them in towelling robes, and that His Serene Highness had bridled at the outrage and declared that her works be outlawed, henceforth and on pain of death, within the bounds of his kingdom. This struck me as precisely how a jealous monarch should behave, and the twin sense of Kelly as both sovereign and subversive was planted in my brain. I was told how remarkable it was that Kelly had deigned to sing, and therefore how natural it was that her yacht-borne duet with Crosby, “True Love,” should have sold a million copies on record. She fondles the end of his squeezebox as they harmonize, but that, I suspect, went over my head, as did their bizarre exchange beside the swimming pool:High Society intro part 1“Gee, I didn’t know that you wanted a husband who would be kind of a high priest to a virgin goddess.”Best of all, my mother pointed out that when Crosby sang “I Love You, Samantha” he did everything—folded his handkerchief, tied his bow tie, wound his wristwatch, filled his cigarette case, and donned his tuxedo, crooning all the while—without a cut. I had never heard of a cut before, or a take. (And, if there is any actor alive today who could reach that extreme pitch of relaxation, I’ve yet to see him.) When the cut finally comes, it is to Kelly, listening at the window of her bedroom. She walks away, overwhelmed; we follow her, then pause, and pull politely back, as she turns and stands there, sheathed in her Oriental robe of yellow-gold. Downstairs, Louis Armstrong laughs and says, “Now we’re gettin’ warm.”
“Oh, stop using those foul words.”
-- Two sides of Grace Kelly
High Society intro part 2
High Society - Well, Did You Evah?
What a Swell Party this is
Who Wants to be a Millionaire
Now You Has Jazz
Original Trailer 1956