Medical teams found Courtney Joy Trueman struggling to breathe after being left in the family Metro as temperatures outside reached 23C (75F). She was unconscious when she was admitted to Tameside General Hospital in Ashton-under-Lyne, where she later died.
Neighbours believe the child's mother, Maria, 31, had placed her in the car on the drive of their house in Dukinfield, Greater Manchester, while she worked in the garden. She strapped the child into the baby seat when the car was not in direct sunlight, considering it a cooler place for her, they said.
Police are believed to be investigating reports that the baby was in the car for up to two hours.
Mrs Trueman and her husband, Andrew, 29, a motor mechanic, have two other daughters and a son.
The child's parents found Courtney obviously unwell and called an ambulance at 2.25pm on Saturday. Paramedics treated the child at the scene before taking her to hospital. She was pronounced dead at 3.55pm.
A post-mortem examination carried out on Sunday has not yet established the exact cause of death.
Yesterday, the NSPCC said there had been rare instances of such deaths in the UK. "Babies easily overheat because their temperature control mechanisms are underdeveloped," said a spokesman. "They should not be left in a car under any circumstances."
A spokeswoman for Greater Manchester Ambulance Service said the call relating to Courtney had been logged as a possible case of sunstroke. The hospital was put on stand-by and the baby was alive when she arrived.
Detective Chief Inspector Eileen Scarratt, of Stalybridge CID, said: "The police are investigating circumstances surrounding the baby's death and that is all I can say at present about this tragedy." Officers have carried out house-to-house inquiries and have examined the family's car.
A neighbour said: "Maria had put the baby in the car while it was still in the shade so she could do the gardening at the side of the house and back. She adored the baby - she was born at home and Maria doted on her. The next day Andy came to the house with CID officers and collected some clothes. He just said he couldn't bear to be in the house."
Another neighbour added: "They have only lived in this street for about a year. But we often saw the children playing in the street with dad running round looking after them."
Earlier this month, a test by the Automobile Association showed that when it was 31C (88F) outside, the temperature inside a car soared to 56C (133F). Even when the outdoor temperature dropped to 27C, the heat inside the car continued rising to 58C. A spokesman said: "The car acts like a radiator, continuing to heat up, and we do see some incredible temperatures inside cars. For a child or pet inside, it would be like sitting in a glasshouse."
Last year an inquest in Norfolk heard how 23-month-old Martha Daniels died after being left in a car when outdoor temperatures topped 21C (70F). Her mother Sarah Daniels, from Litcham, left the child in the car while she did cleaning work. The coroner recorded an open verdict after being told that doctors could find no clear cause of death.Reuse content