Extreme temperatures can injure or kill organisms and can drive evolutionary patterns. Many indices of extremes have been proposed, but few attempts have been made to establish geographic patterns of extremes and to evaluate whether they align with geographic patterns in biological vulnerability and diversity. To examine these issues, we adopt the CLIMDEX indices of thermal extremes. We compute scores for each index on a geographic grid during a baseline period (1961–1990) and separately for the recent period (1991–2010). Heat extremes (temperatures above the 90th percentile during the baseline period) have become substantially more common during the recent period, particularly in the tropics. Importantly, the various indices show weak geographic concordance, implying that organisms in different regions will face different forms of thermal stress. The magnitude of recent shifts in indices is largely uncorrelated with baseline scores in those indices, suggesting that organisms are likely to face novel thermal stresses. Organismal tolerances correlate roughly with absolute metrics (mainly for cold), but poorly with metrics defined relative to local conditions. Regions with high extreme scores do not correlate closely with regions with high species diversity, human population density, or agricultural production. Even though frequency and intensity of extreme temperature events have – and are likely to have – major impacts on organisms, the impacts are likely to be geographically and taxonomically idiosyncratic and difficult to predict.