Sir Jack Brabham's youngest son David said in a statement:
It's a very sad day for all of us. My father passed away peacefully at home at the age of 88 this morning.
He lived an incredible life, achieving more than anyone would ever dream of and he will continue to live on through the astounding legacy he leaves behind.
More top news
The seven-month-old baby girl is believed to have been left in a car in Co Tipperary for several hours.
At times a little fair weather cloud may bubble up - and there will be a fairly brisk southeasterly breeze - but it will still feel hot.
Analysis of data from hospitals in England showed patients were waiting longer for ambulances, treatment and admission.