Courtney Joy Trueman, who was only three months old, was found at her home in Dukinfield, Greater Manchester, on Saturday afternoon suffering from breathing difficulties.
An ambulance crew answering an emergency call to the house found Courtney in a "collapsed state". They rushed her to Tameside Hospital, where she later died.
A post-mortem was carried out but the results have not been released.
Car taken away
It is believed Courtney was in the Austin Metro car, which had been parked in the shade, for about two hours during early afternoon, in temperatures of up to 23°C (75°F).
A spokesman for Greater Manchester police said: "We cannot confirm the baby was in the car, but a car has been taken away that belongs to the family.
"Inquiries are continuing into the circumstances of her death."
Police have interviewed Courtney's parents, Andrew and Maria, who have two other daughters and a son.
Neighbours of the couple said they were shocked. One woman, who did not want to be named, said they seemed a happy family.
She said they had only lived there for a year and kept themselves to themselves but she often saw the children playing in the street with their father.
Cars 'like glasshouses'
Motoring organisations and charities have warned that in-car temperatures can rise to "terrifying levels" in hot weather.
The Automobile Association is currently carrying out tests on heat inside cars at different times of the day.
A spokesman said one result from earlier this month was that on a day when the outside temperature was 31°C (88°F), it soared to 56°C (133°F) inside the car.
And even when the temperature outside dropped to 27°C (81°F), the heat inside the car continued rising, to 58°C (136°F).
"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," the spokesman said.
A spokeswoman for the Royal Society for the Prevention of Accidents said: "Never leave a young child unattended anywhere. It only takes a minute for something to happen."
Northern Ireland
Scotland
Wales
England
Scorching heat kills 48
(10 Aug 98 | Europe)
Open verdict on toddler death
(06 Aug 98 | UK)
Hot weather health warning
(05 Aug 98 | Health)
Heat stroke warning
(31 Jul 98 | Health)
Heat Index reference chart
Greater Manchester Police
RoSPA
Automobile Association
The BBC is not responsible for the content of external internet sites.
Next steps for peace
Blairs' surprise over baby
Bowled over by Lord's
Beef row 'compromise' under fire
Hamilton 'would sell mother'
Industry misses new trains target
Quins fightback shocks Cardiff
(From Sport)
Vodafone takeover battle heats up
(From Business)
IRA ceasefire challenge rejected
Thousands celebrate Asian culture
Christie could get two-year ban
(From Sport)
Colleagues remember Compo
(From Entertainment)
Mother pleads for baby's return
Toys withdrawn in E.coli health scare
Nurses role set to expand
(From Health)
Israeli PM's plane in accident
More lottery cash for grassroots
Pro-lifers plan shock launch
Double killer gets life
Cold 'cure' comes one step closer
(From Health)
Straw on trial over jury reform
(From UK Politics)
Tatchell calls for rights probe into Mugabe
Ex-spy stays out in the cold
Blair warns Livingstone
(From UK Politics)
Smear equipment `misses cancers'
(From Health)
Boyzone star gets in Christmas spirit
(From Entertainment)
Fake bubbly warning
Murder jury hears dead girl's diary
Germ warfare fiasco revealed
(From UK Politics)
Blair babe triggers tabloid frenzy
Tourists shot by mistake
A new look for News Online