Does a rise in temperature decrease the level of GDP in affected countries or the permanent growth rate of their GDP? 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 change from causing them 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. These estimates imply projected future impacts that are three to five times larger than level effect estimates and two to four times smaller than permanent growth effect estimates, with larger discrepancies for initially hot and cold countries.