A San Antonio Fire Department official said they found "stacks of bodies" and no signs of water in the truck, which was found on Monday next to railway tracks in a remote area on the city's southern outskirts.
Sixteen other people found inside the trailer were transported to hospitals for heat stroke and exhaustion, including four minors, but no children were among the dead, the department said.
"The patients that we saw were hot to the touch, they were suffering from heat stroke, exhaustion," San Antonio Fire Chief Charles Hood told a news conference.
"It was a refrigerated tractor-trailer but there was no visible working A/C unit on that rig."
Temperatures in San Antonio, which is about 250 kilometres from the Mexican border, swelled to a high of 39.4C on Monday with high humidity.
San Antonio Police Chief William McManus said a person who worked in a nearby building heard a cry for help and went to investigate.
The worker found the trailer doors partially opened and found a number of dead bodies.
McManus said this was the largest incident of its kind in the city and said three people were in custody following the incident, though their involvement is not yet clear.
A spokesperson for US Immigration and Customs Enforcement said it was investigating "an alleged human-smuggling event" in co-ordination with local police.
The deaths highlight the challenge of controlling migrant crossings at the US-Mexico border, which have reached record highs.
The issue has proven difficult for US President Joe Biden, a Democrat who came into office pledging to reverse some of the hardline immigration policies of his Republican predecessor Donald Trump.Â
Republicans have criticised Biden's border strategy ahead of the midterm congressional elections in November.
Mexican Foreign Minister Marcelo Ebrard called the migrants' suffocation the "tragedy in Texas" on Twitter and said consular officials would go to the hospitals where victims had been taken to help "however possible".
The Honduran foreign ministry said the country's consulates in Houston and Dallas would investigate the incident.
Ebrard said two Guatemalans were hospitalised and Guatemala's foreign ministry said on Twitter that consular officials were going to the hospital "to verify if there are two Guatemalan minors there and what condition they are in".
The I-35 highway near where the truck was found runs through San Antonio from the Mexican border and is a popular smuggling corridor, according to Jack Staton, a former senior official with ICE's investigative unit who retired in December.
In July 2017, 10 migrants died after being transported in a tractor-trailer that was discovered by San Antonio police in a store car park.
The driver, James Matthew Bradley Jr, was sentenced the following year to life in prison for his role in the smuggling operation.
