The seven-month-old had been airlifted to hospital from the village of Dundrum in County Tipperary.
Irish police said emergency services had responded to a 999 call after the child was found “unresponsive”.
She was flown by helicopter to University Hospital in Limerick but pronounced dead a short time later.
It is understood the baby was due to be dropped off at a creche on Thursday morning but did not arrive.
Her father, who works in a local steelworks, is reported to have returned to his car after lunchtime.
Police, who described it as “a personal tragedy” and “very sensitive”, are liaising with the family.
Roger Kennedy, a Fianna Fail county councillor, told the Irish Times: “The whole area is in shock.”
He described the child’s family as “popular” and “well-known” and spoke of “total sadness here”.
Sinn Fein councillor Martin Browne told the paper it had been “the hottest day of the year so far in the area”.
“They are a very nice, very respectable family and it is just a complete tragedy,” he added.