1. When a species experiences a new climate, it can adapt in two main ways: become genetically adapted to the new temperature, or adopt a plastic approach that allows it to survive at a range of temperatures. 2. The constraint on fitness for genetically adapted populations that are exposed to a new temperature has been well studied, but the range of optimal temperatures and their effect on fitness has never been examined across the worldwide distribution of a plastic species. 3. Here, we determined the optimum temperature range of 11 populations of the phenotypically plastic species Drosophila simulans. We measured the influence of temperature on eggs, larvae and adults at six temperatures that span the natural range the flies experience during their primary breeding season. We found no correlation between optimum temperature and native temperature, an effect that is not likely due to laboratory maintenance, suggesting that the species has not locally adapted to temperature. 4. We also found that this species had equal survival and reproductive success at most of the temperatures and life stages that we tested, regardless of the native temperature where the flies originated. 5. Thus, this genetically plastic species has an optimum fitness at a surprisingly wide range of temperatures, and is the first example of a cosmopolitan species exhibiting this large amount of plasticity across its sampling distribution.