Does a permanent rise in temperature decrease the level or growth rate of GDP in affected countries? Differing answers to this question lead prominent estimates of climate damages to diverge by an order of magnitude. This paper combines indirect evidence on economic growth with new empirical estimates of the dynamic effects of temperature on GDP to argue that warming has persistent, but not permanent, effects on growth. We start by presenting a range of evidence that technology flows tether country growth rates together, preventing temperature changes from causing growth rates to diverge permanently. We then use data from a panel of countries to show that temperature shocks have large and persistent effects on GDP, driven in part by persistence in temperature itself.