(1) Background: High ambient temperatures are associated with increased morbidity and mortality rates, and some evidence suggests that high temperatures increase the risk of road crashes. However, little is known regarding the burden of road crashes attributable to no-optimal high temperatures in Australia. Therefore, this study examined the effects of high temperatures on road crashes using Adelaide in South Australia as a case study. (2) Methods: Ten-year daily time-series data on road crashes (n = 64,597) and weather during the warm season (October–March) were obtained between 2012 and 2021. A quasi-Poisson distributed lag nonlinear model (DLNM) was used to quantify the cumulative effect of high temperatures over the previous five days. The associations and attributable burden at moderate and extreme temperature ranges were computed as relative risk (RR) and attributable fraction. (3) Results: There was a J-shaped association between high ambient temperature and the risk of road crashes during the warm season in Adelaide, and pronounced effects were observed for minimum temperatures. The highest risk was observed at a 1 day lag and lasting for 5 days. High temperatures were responsible for 0.79% (95% CI: 0.15–1.33%) of road crashes, with moderately high temperatures accounting for most of the burden compared with extreme temperatures (0.55% vs. 0.32%). (4) Conclusions: In the face of a warming climate, the finding draws the attention of road transport, policy, and public health planners to design preventive plans to reduce the risk of road crashes attributable to high temperatures.