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Global food demand is increasing with the rapid growth of the worlds population and improvement in living standards. To meet this demand, crop yields need to increase but climate change presents a potential threat. Genetic and agronomic strategies are helping agriculture adapt to climate change, but introducing new genetic traits into crops is time-consuming and costly. Process-based biophysical modelling is a powerful tool for targeting and accelerating development of new synthetic cultivars, and we have used it to identify the traits of rainfed wheat ideotypes and suitable sowing dates needed to adapt to future climate change in south-eastern Australia. Our simulations involved two Global Climate Models (GCMs) with the driest conditions under a high emission scenario of Representative Concentration Pathway (RCP) 8.5 We compared simulated yields under future climate with those under historical climate with and without changes in cultivar and sowing date. Our results show that wheat yield for the reference cultivar would decrease on average by 23% and 38% in 2061-2100 under RCP8.5 at two contrasting sites (wet and dry, respectively). Ideotypes with an early flowering date, longer grain filling period, larger radiation use efficiency, larger maximum grain size and faster potential grain filling rate, sown on the optimum sowing date proved to be effective at the wet site in reversing these declines, leading to an average yield increase of 20-24% for both GCMs. However, improving cultivars and altering sowing times would have little impact for a drier GCM at the dry site. Although there is some uncertainty in simulations related to the genetic coefficients used in the crop model, climate projections and emission scenarios, we demonstrate that it is possible to enhance wheat production under a future climate if a cultivar with a longer grain filling period and larger yield component parameter was adopted in eastern Australian wheat-growing areas.