Fifty-four years later, one might suppose that the famous dress came on to the stage of its own accord, as if it had life as well as destiny. But yes, in 1962, there was a warm body inside it. This was 19 May 1962, and Marilyn Monroe was bringing happy birthday wishes to the president of the United States. She was 10 days early: the actual birthday of John F Kennedy, his 45th, would not be until 29 May. So what? The Democratic party wanted to have a super fundraiser at Madison Square Garden in New York City, so they needed not just JFK himself, but a hook and bait. The birthday was a pretext until the breathy song, “Happy birthday, Mr President ...”

That was Marilyn Monroe. But did the Dems ask her or did the president himself arrange it? Sometimes a president can be an instrument in his own PR. Marilyn would be 36 on 1 June, which would prove to be her last birthday. On 5 August, she was found dead in her bed in Brentwood with just a sheet around her.

Happy Birthday Mr President feels so directed an incident, you have to wonder who was running the show. Was it Peter Lawford, the president’s brother-in-law, who seems to have been the onstage host for the event, dapper in his tux, looking off into the wings, waiting for a bright light, calling for her but she never shows, until at last he can welcome “the late Marilyn Monroe” – does he hear what he’s saying?

Or was it Marilyn’s own doing? There is a thought now, decades later, that says she was the victim of her time, that she was a wistful actor who wanted to play Chekhov or O’Neill. But still, you have to note how, time and again, hanging on to what was called her career, she did these far-fetched things that catered to male dreams – such as playing Sugar Kane in Some Like it Hot, kissing Tony Curtis and being the dumb blond in a dirty joke for us.

You can say that only demonstrates her victimhood and makes her wishing more wistful. But then you have to see the plain delight with which she did these preposterous things, these moments, as if she could not resist or do without the comfort that came with the gasps and the whistles at Madison Square Garden when she came into the platinum light, shrugged off her wrap and stood there, with her massed blonde waves jutting off to one side, like the control on tower an aircraft carrier, in a dress that could have been painted on her. And she did not seem like the hesitant neurotic of fame and constant lateness when she broke into the birthday song. Just take a look. She seems happy, and an actress is hired to give us some sort of good feeling. This is maybe her greatest moment – the most reckless – and she knows it, even if the summer of 1962 is her hell.

That dress didn’t just happen. It was the work of Jean Louis. Born in France in 1907, he had come to the US as a fashion designer and then got into the movies. He did work for the Duchess of Windsor, and he also created the black satin dress worn by Rita Hayworth in Gilda (1946). Hayworth does a restrained striptease (drawing off her elbow-length gloves) in the Put the Blame on Mame number, which was thought daring in its day. After the war, a pressure grew in movies (it was censorship fighting desire) in which we were asked to imagine what a woman would look like without clothes. It was as if there was a cultural blooming that had to break out of its sheath.

Facebook Twitter Pinterest The dress on display at Christie’s in Los Angeles, in 1999. Photograph: Scott Nelson/EPA

Louis was an important figure in that history: he also did the black bathing suit that Deborah Kerr wears on an Hawaiian beach in From Here to Eternity, when she’s rolling in the surf with Burt Lancaster. That scene looks charming now, but in 1953 it was close to the outrage audiences were urging. There was a silly British gangster film in 1960, Too Hot to Handle, where Jayne Mansfield wore such a dress, and about which the story was promoted that the movie was so risque a few extra sequins had had to be painted on to the film to protect (or fetishise) Jayne’s nipples. But the Happy Birthday Mr President dress was the climax of this quest.

That summer was a frenzied time for Marilyn, and there are signs of how far she yearned to break out of not just a dress, but every setup that imprisoned her. Twentieth Century Fox put her in a new picture, Something’s Got to Give, for which she shot a promotional nude swimming scene – though censorship would not have allowed the sequence. It was as if she was breaking out already. Her illnesses or her anxieties slowed the film but then she took that unexpected excursion to New York to sing to JFK – and seemed camera-ready. Fox fired her and replaced her with Lee Remick.

That swimming pool scene and a silent screen test she had done with George Cukor are the most radiant and eloquent things she ever put on moving film. And in the same summer, with Bert Stern, she shot some semi-nude still pictures – this became the famous “last sitting” where she seems to look like a would-be Kennedy or a plaintive beauty more appealing for being freed from so many stereotypes.

Facebook Twitter Pinterest Marilyn Monroe still wearing the dress, with Steve Smith, Kennedy’s brother-in-law, at a reception at Madison Square Garden. Photograph: Cecil Stoughton/AP

There were also stories of a terrible weekend at the Cal-Neva Lodge, on the borders of California and Nevada, where Marilyn was passed around a circle of powerful men. The details are not clear, but you do not really want clarity. She was dead in just over a week, and that death (ahead of JFK’s) would have so many stories told about it that we’ll never know.

The dress remains, and I daresay it has provenance, although we are accustomed to be wary with such relics. Every now and then, people buy the Rosebud sled from Citizen Kane, amid mounting suspicion that there were several sleds. Why not? It was a movie, not a life in Colorado.

The dress itself, with all its inserted rhinestones, was said to have cost $12,000 in 1962. In 1999, it was sold for $1.3m (then £790,000), and now it is up for auction again, with some other Monroe mementoes. Should it be purchased by the Smithsonian, or will some Trump-like figure buy it, to wonder if any woman he knows would fit in it? The dress must be cold now – it’s likely kept in a temperature-controlled vault – to guard against decay or disintegration. But one night in May 1962 it would have been the object of farcical preparation and infinite imagining. And for a few moments at least, it was warm.