This surprised me, there was a 1939 film called “Some Like It Hot”! Not to be confused with the Billy Wilder classic this was later retitled "Rhythm Romance". The movie starred Bob (Leslie) Hope and Shirley Ross (Bernice Gaunt) and together they introduced "The Lady's In Love With You" (Burton Lane - Frank Loesser). In the film it was sung by Shirley with the Gene Krupa Orchestra.

We continue with the unusal as Glenn Miller's voice is actually heard on "The Lady's In Love With You" along with vocalist Tex (Gordon) Beneke. In 1939 the single peaked at number two. Wikipedia "Glenn Miller went missing on December 15, 1944, while flying to France from England. After World War Two, the United States Army Air Force decommissioned the Glenn Miller-led Army Air Force band. The Miller estate authorized an official Glenn Miller "ghost band" in 1946. This band was led by Tex Beneke who as time went on had more prominence in the band's identity. It had a make up similar to Glenn Miller's Army Air Force Band, having a large string section. The orchestra's official public début was at the Capitol Theatre on Broadway where it opened for a three-week engagement on January 24, 1946. Henry Mancini was the band's pianist and one of the arrangers."