Three people were in custody after 46 bodies were found in a lorry trailer containing suspected migrants on the outskirts of San Antonio.
However, police chief William McManus said it was unclear if those arrested were connected with human trafficking.
Some sixteen people were taken to hospitals after the lorry was found on a remote back road near the south-west Texas city.
A city worker at the scene was alerted to the situation by a cry for help shortly before 6pm (12am BST)on Monday, Mr McManus said, adding that officers arrived to find a body on the ground and a partially opened gate to the trailer.
Of the 16 taken to hospitals with heat-related illnesses, 12 were adults and four were children, said fire chief Charles Hood. The patients were hot to the touch and dehydrated, with the trailer lacking water or air-conditioning, he said.
“They were suffering from heat stroke and exhaustion,” Mr Hood said. “It was a refrigerated tractor-trailer, but there was no visible working AC unit on that rig.”
San Antonio Mayor Ron Nirenberg said the 46 who died had “families who were likely trying to find a better life”.
“This is nothing short of a horrific human tragedy,” Mr Nirenberg added.
Those in the trailer were part of a presumed migrant smuggling attempt into the US and the investigation was being led by Homeland Security Investigations, Mr McManus said.
It may be the deadliest tragedy among thousands where people have died attempting to cross the border from Mexico in recent decades.
Ten migrants died in 2017 after being trapped inside a truck that was parked at a Walmart in San Antonio. In 2003, 19 migrants were found in a sweltering truck south-east of San Antonio.
Lorries emerged as a popular smuggling method in the early 1990s amid a surge in US border enforcement in San Diego and El Paso, Texas, which were then the busiest corridors for illegal crossings.
Before that, people paid small fees to mom-and-pop operators to get them across a largely unguarded border. As crossing became exponentially more difficult after the 2001 terror attacks in the US, migrants were led through more dangerous terrain and paid thousands more.
Heat poses a serious danger, particularly when temperatures can rise severely inside vehicles.
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