Global warming is a worldwide and protracted phenomenon with heterogeneous local economic effects. We propose a dynamic economic assessment model of the world economy with high spatial resolution to assess its consequences. Our model features several forms of adaptation to local temperature changes, including costly trade and migration, local technological innovations, and local natality rates. We quantify the model at a 1o × 1o resolution and estimate damage functions that determine the impact of temperature changes on a region’s fundamental productivity and amenities conditional on local temperatures. Welfare losses from global warming are very heterogeneous across locations, with 20% losses in parts of Africa and Latin America but also gains in some northern latitudes. Overall, spatial inequality increases. Uncertainty about average welfare effects is significant but much smaller for relative losses across space. Migration and innovation are shown to be important adaptation mechanisms. We use the model to study the impact of carbon taxes, abatement technologies, and clean energy subsidies. Carbon taxes delay consumption of fossil fuels and help flatten the temperature curve but are much more effective when an abatement technology is forthcoming.