Climate change may be a major threat to global biodiversity, especially to tropical species. Yet, why tropical species are more vulnerable to climate change remains unclear. Tropical species are thought to have narrower physiological tolerances to temperature, and they have already experienced a higher estimated frequency of climate-related local extinctions. These two patterns suggest that tropical species are more vulnerable to climate change because they have narrower thermal niche widths. However, no studies have tested whether species with narrower climatic niche widths for temperature have experienced more local extinctions, and if these narrower niche widths can explain the higher frequency of tropical local extinctions. Here, we test these ideas using resurvey data from 538 plant and animal species from 10 studies. We found that mean niche widths among species and the extent of climate change (increase in maximum annual temperatures) together explained most variation (>75%) in the frequency of local extinction among studies. Surprisingly, neither latitude nor occurrence in the tropics alone significantly predicted local extinction among studies, but latitude and niche widths were strongly inversely related. Niche width also significantly predicted local extinction among species, as well as among and (sometimes) within studies. Overall, niche width may offer a relatively simple and accessible predictor of the vulnerability of populations to climate change. Intriguingly, niche width has the best predictive power to explain extinction from global warming when it incorporates coldest yearly temperatures.