The migrants died “excruciatingly painful” deaths, having suffocated in the container en route from Belgium to Purfleet in , a judge said.
Ronan Hughes, 41, and Gheorghe Nica, 43, played “leading roles” in the smuggling conspiracy and were jailed for 20 and 27 years respectively.
Eamonn Harrison, 24, who towed the trailer to the Belgian port of Zeebrugge before their journey to the UK, was sentenced to 18 years.
Maurice Robinson, 26, was given 13 years and four months, having collected the trailer and opened it in an industrial estate to find the migrants dead.
Sentencing, Mr Justice Sweeney said: “I have no doubt that the conspiracy was a sophisticated, long-running and profitable one to smuggle mainly Vietnamese people across the channel.”
He said on the fatal trip the temperature had been rising along with the carbon dioxide levels throughout, hitting 40C (104F) while the container was at sea on .
“There were desperate attempts to contact the outside world by phone and to break through the roof of the container,” the judge said.
“All were to no avail and, before the ship reached Purfleet, [the victims] all died in what must have been an excruciatingly painful death.”
The victims had used a metal pole to try to punch through the roof but only managed to dent the interior.
The court heard some of their final desperate phone messages, including one where a man spoke with ragged breaths as he apologised to his family.
Justice Sweeney added: “The willingness of the victims to try and enter the country illegally provides no excuse for what happened to them.”
During the trial, jurors were given a snapshot of the victims – who included a bricklayer, a university graduate and a nail bar technician – and their dreams of a better life.
Many of their families borrowed heavily to fund their passage, relying on their potential future earnings once they got into the UK.
The father of Nguyen Huy Tung, one of two 15-year-olds in the container, later learned of his son’s death Divorced dating apps via social media.
Harrison, of Newry, County Down, claimed he did not know there were people in the trailer when he towed it to the Belgian port, and that he watched “a wee bit of Netflix” in bed as they were loaded on.
Robinson gave a thumbs-up in reply. When Robinson stopped on a nearby industrial estate, he found that the migrants were all dead.
His barrister said Robinson, who admitted manslaughter, being part of the trafficking plot and money laundering, was “horrified by what he saw”.
The trial examined three smuggling attempts by the gang – two that were successful on 11 and 18 October, and the final trip on 23 October.
When Robinson discovered the bodies, there was a series of telephone conversations between him and Nica and Hughes, of Tyholland, County Monaghan, Ireland, before the driver eventually dialled 999.
Mr Justice Sweeney said that in the conspiracy “two played leading roles, namely – in order of importance – Hughes and Nica”.
He accepted Hughes was “not at the very top of the conspiracy” but said his role was “pivotal. in that he ran a haulage business and supplied the trailers and drivers used to transport the migrants”.
The judge said Nica “recruited and paid the drivers whose job it was to collect the migrants when they reached the drop-off site in this country and to drive them to the safe house(s) where they were to be held until payment”.
Mr Justice Sweeney told the defendants jailed for manslaughter they would serve two-thirds of the term in custody, instead of the usual half.
Earlier this month, Gazmir Nuzi, 43, of Barclay Road, Tottenham, north London, was sentenced, having admitted his limited role in the people-smuggling operation. It was accepted he was not a member of the organised crime group behind the smuggling operation.
Det Ch Insp Daniel Stoten said: “May this serve as a warning to those who think it’s OK to prey on the vulnerabilities of migrants and their families, transporting them in a way worse than we would transport animals.