This paper shows that separating persistent (permanent) temperature changes from transitory weather fluctuations can reshape our understanding of the macroeconomic costs of warming. Using a Kalman filter state-space decomposition, it separates temperature into a permanent component and transitory weather fluctuations, and links the permanent component to trend output using a panel cointegration and error-correction framework. A one-degree Celsius higher permanent temperature is associated with a significant decline in the long-run level of output, with full adjustment unfolding over multiple decades to a century. Decomposing aggregate output into population and output per capita reveals that the long-run output losses operate primarily through demographic adjustment in the full sample, while in advanced economies, both long-run output per capita and population decline as the climate warms. Economies with higher capital intensity and more durable capital stocks experience larger long-run per capita output losses. These findings suggest that long-run economic vulnerability to persistent warming is more broadly distributed across rich and poor countries than the short-run weather literature implies, reflecting differences in capital structure. They complement rather than contradict the well-established finding that developing countries are more exposed to short-run weather shocks.