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Globally, the impacts of anthropogenic climate change can displace species into more favourable climates. Semi‐arid desert specialists, such as the sandhill dunnart, Sminthopsis psammophila, are typically susceptible to rainfall deficits, wildfires and extreme temperatures caused by anthropogenic climate change. We first used maximum entropy (MaxEnt) species distribution models (SDMs) to predict the current distribution of S. psammophila. Between 2016 and 2018, we ground validated the model's predictions throughout Western Australia, confirming S. psammophila in 18 locations in which it was predicted to occur. The predicted distribution of S. psammophila appears mostly constrained to within its known range. However, S. psammophila was verified 150 km north of its range in Western Australia and connectivity between the South Australian populations was correctly predicted. In 2019, we used updated occurrence data to project SDMs for S. psammophila during the mid‐Holocene, present day and under two future representative concentration pathways (RCPs) of RCP 4.5 (an optimistic emissions scenario) and RCP 8.5 ("business as usual") for 2050 and 2070. By 2050 (RCP 8.5), almost all Western Australian Great Victoria Desert (WAGVD) habitat is predicted to be unsuitable for S. psammophila. By 2070 (RCP 8.5), the climates of the WAGVD and Yellabinna Regional Reserve populations are predicted to become unsuitable, and the species' geographical range is predicted to contract in Australia by 80%. However, the 2070 (RCP 4.5) scenario predicts that this contraction could be halved. As a sandy desert specialist, the distribution of S. psammophila is geographically limited at its southern bounds due to the cessation of suitable spinifex (Triodia spp.) habitats, and so further extension of the range southwards is not possible. Sympatric desert species may be similarly affected, and we suggest that SDMs will be a useful tool in helping to predict the effects of climate change on their distributions. [ABSTRACT FROM AUTHOR]