To thrive and expand, corals required warm temperatures, good light levels and a naturally occurring mineral called aragonite.
The team found that although climate change could make southern areas more favourable for growth in terms of temperature and aragonite, it was unlikely there would be enough light during the winter months for coral reefs to become established.
To meet the light requirements, scientists predicted that corals would need to grow in increasingly shallower water relative to their distance from the equator - an estimated 60cm for every degree of latitude beyond the equator.
Growth in shallow waters made coral more prone to damage from waves and swells, extreme changes in salinity and competition with other organisms.
The researchers also suggested that activities such as algal blooms, agricultural runoff, urban development and dredging would further reduce light levels and further limit the possibility that corals will survive in temperate seas.
Co-author Dr David Aguirre, of Massey University's Institute of Natural and Mathematical Sciences, said the study was the first to look at whether rising ocean temperatures could enable coral spread in Australia and New Zealand.
"Most of the energy these corals need to survive comes from sunlight and light is not predicted to respond to climate change the same way ocean temperature will."
His colleague and study co-author, Dr Paul Muir, of the Museum of Tropical Queensland in Townsville, told Australia's ABC Online there had been a popular idea that warming would "just shift everything southwards or northwards".
"Everything would be apples and you'd probably end up with corals growing in Sydney Harbour if we were lucky," he said."It doesn't look like it's going to be an option for this group of corals."
Their study was published in the leading scientific journal, Science.
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