Emily France and her son, Owen, were already aboard a United plane, waiting to depart Denver International Airport, when the trip was delayed due to refueling and a reroute caused by bad weather, the mother said.
That's when temperatures in the plane's cabin appeared to spike, France said, as she frantically tried to cool her infant off.
France estimates that she and Owen were on the plane for about two hours, and that the airline appeared completely unprepared to handle the situation, she said. France was allowed to exit United's aircraft for about 20 minutes, she added, but she was then asked to return to still-sweltering temperatures for takeoff.
That's when she said Owen "went limp" in her arms.
"This should never have happened," United said in a statement to CNBC. "We are profoundly sorry to our customer and her child for the experience they endured. We are actively looking into what happened to prevent this from occurring again."
Owen has since been released from the hospital and is now at home, healthy, with his mom, France has told local media.
Colorado experienced a heatwave that last week brought record-breaking temperatures of around 100 degrees. The National Weather Service said the temperature in that area on Thursday was closer to 90 degrees.
This isn't United's first incident with its passengers of late either.
Other public-relations nightmares include when two teenage girls were kicked off a flight after a gate agent deemed their leggings inappropriate. Then, a video went viral of a bloodied passenger being dragged off an overbooked flight.
Most recently, a scorpion stung a man aboard a United flight from Houston to Calgary.