Climate change is already impacting several development outcomes, including economic growth, human health and mortality, agricultural productivity and even conflict. Moreover, the impact of climate change is expected to be unevenly distributed across locations and population groups. In particular, the worst effects of climate change are expected to be felt in low-income countries. Similarly, within countries, the most vulnerable to these effects are typically low-income regions and households. While the literature to date has provided evidence of the between-countries inequality-increasing effect of global warming, evidence for inequality within countries remains limited. In this paper, we empirically explore the connection between climate change and long-run distributional dynamics within countries. To do so, we first build a global panel dataset combining gridded data on climate variables with gridded population data, and country-level data on a range of inequality measures and development outcomes. We use these data to test climate effects on several dimensions of inequality, including the (interpersonal) distribution of income, using traditional Gini coefficients, indices of concentration of both income and wealth, proxies of inequality in the spatial distribution of economic activity within countries, and measures of inequality in life expectancy. Our evidence shows a clear positive and statistically significant relationship between higher temperatures and increases in different measures and dimensions of inequality. The role of higher temperatures is robust to a wide range of controls, different specifications and estimation techniques. We complement our country-level analysis with an exploratory analysis at the subnational level for selected countries (US, Russia and Spain).