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Preterm birth (born before 37 completed weeks of gestation) is one of the leading causes of death among children under 5 years of age. Several recent studies have examined the association between extreme temperature and preterm births, but there have been almost no such studies in arid Australia. In this paper, we explore the potential association between exposures to extreme temperatures during the last 3 weeks of pregnancy in a Central Australian town. An immediate effect of temperature exposure is observed with an increased relative risk of 1%-2% when the maximum temperature exceeded the 90th percentile of the summer season maximum temperature data. Delayed effects are also observed closer to 3 weeks before delivery when the relative risks tend to increase exponentially. Immediate risks to preterm birth are also observed for cold temperature exposures (0 to -6 degrees C), with an increased relative risk of up to 10%. In the future, Central Australia will face more hot days and less cold days due to climate change and hence the risks posed by extreme heat is of particular relevance to the community and health practitioners.