Three of the migrants found were taken to Methodist Hospital Metropolitan and are in stable condition, according to a spokesperson for Methodist Healthcare.
Heat poses a serious danger, particularly when temperatures can rise severely inside vehicles.
High temperatures in the San Antonio area ranged from the high 90s to low 100s on Monday, according to the National Weather Service.
According to KSAT TV channel, the vehicle was discovered next to rail tracks in San Antonio's Southwest Side.
A large number of emergency responders, including police, fire, and ambulance services, could be seen surrounding the large truck.
San Antonio's Police Chief William McManus said the investigation had now been handed over to federal agents and three people were being held in custody.
Blame game begins
Mexico's Foreign Minister, Marcelo Ebrard, said the country's consul was en route to the site of the discovery, but added that the victims' nationalities were still unknown.
Texas's Republican Governor Greg Abbott blamed US President Joe Biden for the deaths, describing them as a "result of his deadly open border policies".
Beto O'Rourke, the Democratic candidate running against Mr Abbott, said the reports were devastating and called for urgent action to "dismantle human smuggling rings and replace them with expanded avenues for legal migration".
Illegal immigration - a growing problem
Monday’s discovery may be the deadliest tragedy among thousands who have died attempting to cross the US border from Mexico in recent decades. Ten people died in 2017 after being trapped inside a truck that was parked at a Walmart in San Antonio. In 2003, 19 others were found in a sweltering truck southeast of San Antonio, the Associated Press reported.
Big rig trucks 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.
Prior to that, people paid small fees to mom-and-pop operators to get them across a largely unguarded border.
As crossing became much more difficult after the 2001 terror attacks in the US, individuals were led through more dangerous terrain and paid thousands of dollars more.
(with inputs from AP)
