The surprising discovery suggests that the birds are preparing their offspring for warm conditions after they hatch.
Scientists collected eggs and incubated them in controlled conditions, playing recordings of the incubation song.
Compared to a control group, hatchlings that received these calls grew more slowly and coped better in the heat.
Writing in the journal Science, the researchers say this is the sort of adaptation that could help animals acclimatise to rising global temperatures.
"It doesn't mean that they will still be able to breed at extreme temperatures - this was within the range they currently experience," said the paper's lead author Mylene Mariette, from Deakin University in Geelong.
"But what's encouraging is that it's a strategy that the birds use to adjust the growth of their offspring to temperature, that we didn't know about."
It is also the first time that singing to unborn chicks has been shown to yield such long-term results.
Previous studies have mostly concentrated on egg-bound embryos learning particular calls from their parents.
"We knew it could have some short-term effects on cognition and learning, but our study is the first to show that is has an effect on their growth and their development - and that those effects last until adulthood," Dr Mariette told BBC News.
"It means that the acoustic environment before birth has more impact than we thought."
She first noticed the rhythmic, high-pitched calls while making field recordings during her PhD.
"I was looking at how the parents talk to each other to coordinate parental care. That's when I noticed that sometimes when a parent was by itself in the nest, incubating the egg, it produced a quite different call.
"I wondered - hmm, are they talking to their eggs?"
When she started to study this squeaky serenade in detail, combing through Dr Mariette found that the birds were specifically singing it in the few days before eggs hatched - and only when the day's ambient temperature rose above about 26C.
"It's not that they do it spontaneously whenever it's hot; they do it when it's hot and when the embryos could potentially hear them," she said.
To figure out the specific effect of the calls, Dr Mariette and her colleague Katherine Buchanan used zebra finches living in the university's outdoor aviaries.
They collected eggs and, for the final five days of their incubation, played them either a recording of the birds' special egg-song, or a typical parent-to-parent call instead.
As soon as they hatched, the 175 chicks were returned to various nests and the team observed the youngsters' development in detail.
To begin with, the two groups were indistinguishable; the song hadn't changed the chicks' hatching weight.
Within a few days, however, that changed.
"We found that, depending on whether or not they had heard the 'hot call' from their parents, they reacted differently to heat," Dr Mariette explained.
"They adjusted their growth to temperature differently, and also solicited food from their parents differently."
Specifically, the "heat song" seemed to make the chicks develop slower - and remain lighter - if their nest was in a hot corner of the aviary.
Being a lightweight is generally bad news in evolutionary terms, but when the researchers followed the finches' fortunes into adulthood, it proved the opposite: those lighter birds that grew up in hot nests produced significantly more fledglings than their heavier childhood companions.
Furthermore, the chicks that were primed with a "heat song" in the egg went on to prefer warmer nesting spots.
"It's as if the parents are preparing the chicks for the temperature they will experience after hatching," said Dr Mariette.
It is a mystery, she added, how being smaller gives the birds an advantage in the heat. But it may be because growing in hot conditions is costly for the body, placing more oxidative stress on tissues - so staying small becomes a better strategy.
This could also help explain why, as global temperatures rise, wild bird populations in general are slowly shrinking - though mostly, that process has been seen to have negative consequences for the species involved.
Whatever their evolutionary implications, the Deakin team's findings are an intriguing case of communication between parents and unborn offspring.
Nicola Hemmings, a research fellow studying bird reproduction at Sheffield University in the UK, said the experiments were elegantly designed and the results convincing.
"They've shown that not only can parents teach their offspring a call while they're still in the egg - but that they're giving them quite specific information about the environment they're about to hatch into," she told the BBC.
Just like the study's authors, Dr Hemmings said she was fascinated by what might be driving the changes in the chicks' development.
"They're not actually thinking, 'Mum says it's hot out there, I better take it slow when I get outside!' But it's having some kind of physiological effect on their body which is making their growth rate slow.
"Does it have a hormonal basis? Is it a stress response? That would be the interesting thing to look at next."
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When the weather is hot, zebra finches in Australia sing to their eggs - and these "incubation calls" change the chicks' development, a study has found.