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.
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.”
“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.
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.