In a recent article in this journal, Francesco Bosello, Roberto Roson, and Richard Tol make the surprising prediction that the first stages of global warming will, on balance, save a large number of lives. Bosello et al. fail to substantiate this remarkable estimate, and they make multiple mistaken or misleading assumptions. They rely on research that identifies a simple empirical relationship between temperature and mortality, but ignores the countervailing effect of human adaptation to gradual changes in average temperature. While focusing on small changes in average temperatures, they ignore the important health impacts of extreme weather events such as heat waves, droughts, floods, and hurricanes. They extrapolate this pattern far beyond the level that is apparently supported by their principal sources, and introduce an arbitrary assumption that may bias the result toward finding benefits from warming.