Mexican sunflower [Tithonia diversifolia (Hemsl.) A. Gray] is an invasive plant, native to the New World, and an exemplary conflict species. It has been planted widely for its ornamental and soil fertility enhancement qualities and has become a notorious environmental weed in introduced habitats. Here we use a bioclimatic niche model (CLIMEX) to estimate the potential global distribution of this invasive plant under historical climatic conditions. We apply a future climate scenario to the model to assess the sensitivity of the modeled potential geographic range to expected climate changes to 2050. Under current climatic conditions, there is potential for substantial range expansion into southern Europe with moderate climate suitability, and in southern China with highly suitable climates. Under the near-term future climate scenario, there is potential for poleward range expansion in the order of 200 to 500 km. In the tropics, climatic conditions are likely to become less favorable due to the increasing frequency of supra-optimal temperatures. In areas experiencing Mediterranean or warm temperate climates, the suitability for T. diversifolia appears set to increase as temperatures warm. There are vast areas in North America, Europe, and Asia (particularly China and India) that can support ephemeral populations of T. diversifolia. One means of enjoying the aesthetic benefits of T. diversifolia in gardens while avoiding the unwanted environmental impacts where it invades is to prevent its spread into areas climatically suitable for establishment and only allow it to be propagated in areas where it cannot persist naturally.