Anirudha Bhattacharya and Balaji Vitthal's book on R D Burman has a reference to the tune of Thandi Hawayein having its original roots to the theme song of Algiers(1938).
Charles Bayer crooned “C’est la vie” in Algiers(1938) without even realizing what a big chain of inspirations he had set for the next generation of Indian music makers. The tune was also used as an instrumental during the credit title at the start of the movie and then later, of course, Bayer sang it in his own baritone polishing his shoes and looking out of the window.
S D Burman indeed might have been hugely influenced by that tune. His first composed duet of Kishore Kumar and Geeta Dutt- Ek hum aur dusre tum- in Pyar(1950), starts with Kishore humming the C’est la vie tune. The song was tuned into an altogether different parameter though. But the foundation of a bigger and better manifestation of that tune was ready for S D.
A year later came Najawan(1951)- where S D Burman simply bettered and over manoeuvred the Algiers tune to make the evergreen “Thandi hawayein”. The starting humming by Lata sticks to the basic tune crooned by Charles Bayer (same as what Kishore had done a year ago) and the mukhda is a simple manifestation of that tune with clever changes here and there and transforming it to a different feel of a composition altogether. This sets the pace- Thandi Hawayein tune, the root of which belonged to the Algiers song- has been the most inspiring Hindi tune ever for the composers.
N Dutta was an assistant to S D Burman in the early 50s before he made mark of his own as an independent music director. He was very much there around S D Burman when the Naujawan song was done. No surprise, he chose to manoeuvre the tune for his own in Jaal Saaz(1959) with “Pyar ka jahan ho”. The song starts with an accordion piece simply playing the “Thandi Hawayein” tune only. The antaras of the song were again highly resembling to those of Thandi Hawayein.
Madan Mohan took a small leaf out of the Thandi Hawayein tune to make “Yehi hai tamanna” in Aapki Parchhaiyan(1964).
Roshan simply reinvented the tune to make “Rahein na rahe hum” in Mamta(1966). Frankly speaking, the finest remake of “Thandi Hawayein” tune ever, Roshan Lal recreated the tune without even making anyone realizing the root of the same. And then, it was again Lata Mangeshkar who delivered the job.
Sonny Rahul Dev Burman used “Thandi Hawayein” connect more than occasionally. While “Naghma humara” from Bundalbaaz(1976) might carry a shade of influence, “Sun zara shokh haseena” from Harjaee(1981) is nothing but a recreation of “C’est la vie” in all aspects. It would take really an expert’s ear to find out the root of the tune again.
Very late in his career, RD made the second best adaption of Thandi Hawayein tune (first for me being Rahein na rahe hum of course)- Sagar kinare. A silght, delicate reconnect to his father’s tune, but then, a master work nonetheless. He had a couple of years ago made "Humein raaston ki zaroorat" in Naram Garam which followed the same tune again.Thandi Hawayein might not have been an altogether original a tune, but it had influenced a generation in a manner even its original source could not.