"This is everyone's worst nightmare," said Larry McKinnon, spokesperson for the Hillsborough sheriff's office, according to NBC affiliate WFLA.
"It doesn't matter whether you're an average citizen on the street or seasoned law enforcement. It's never easy. It touches everyone's heart when something like this happens."
Investigators who spoke to the station said Jacob's half sister was "distraught" when she discovered the toddler during a break.
"Who can take that information, you know? It's gut-wrenching. It's physically debilitating. There's no way around it," McKinnon told WFLA, when asked how the child's parents were doing.
"It's difficult. It's difficult for all of us. We all have kids, we all have children. And we all work hard to try to make sure that the public's educated. We remind ourselves, we remind our family, we remind our people that pick up our kids - look back there and check."
A sheriff's office news release details the incident, stating that deputies were called to a shopping centre in Brandon, which is about 20km from Tampa, Florida, at about 2.40pm, in reference to "a child found locked in an unattended vehicle."
Paramedics also responded to the scene and transported the child to a hospital, where he later died.
"Homicide detectives and crimes scene investigators were called to the scene and are now conducting an ongoing criminal investigation," the release states.
Preliminary information indicates that the victim's half sister arrived at work with Jacob, the release states. She then "went inside her place of employment and left the child unattended in the vehicle."
After returning to her car and finding Jacob, the woman got him out of the vehicle and carried him to a dialysis centre in the shopping centre. First aid was administered, and Jacob was taken to a hospital, where he later died.
No charges had been filed Tuesday, according to a sheriff's office. Authorities were speaking to the 21-year-old woman as well as other witnesses.
"We're going to leave no stone unturned in making sure we know every single detail about what happened," McKinnon, the spokesman, told the Tampa Bay Times, which described the scene at the child-care centre.
The National Weather Service estimated that the outside temperature in the area was about 32C about 2.30pm Tuesday.
"Check the back seat, check your vehicles before you go inside - those campaigns have been throughout the country yet we continue to still see this tragic thing happen," McKinnon told the Times.
"This certainly should be a reminder of what we need to do when transporting our children."
There were more than 30 heat stroke deaths involving children who were left in cars in 2016, according to noheatstroke.org, a website that tracks such incidents. There have been two in 2017, a total that included the death of Jacob Manchego, according to the site.
The other 2017 death involved a boy who was left in a car in South Florida, the site noted.
