Not wanting to wake him after a long car journey, the couple left the child asleep while they want upstairs for a nap in the western town of Nenzing.
Later the boyfriend rushed down to the car, which was in a secluded spot, and found the child's lifeless body, Vorarlberg state police said.
"An autopsy... in Innsbruck established the cause of death as heat stroke," a statement said.
The couple are receiving counselling.
Temperatures at the time were around C30 (86 Fahrenheit).