Climate change and inequality are critical and interrelated defining issues for this century. Despite growing empirical evidence on the economic incidence of climate policies and impacts, mainstream model-based assessments are often silent on the interplay between climate change and economic inequality. For example, all the major model comparisons reviewed in IPCC neglect within-country inequalities. Here we fill this gap by presenting a model ensemble of eight large-scale Integrated Assessment Models belonging to different model paradigms and featuring economic heterogeneity. We study the distributional implications of Paris-aligned climate target of 1.5 degree and include different carbon revenue redistribution schemes. Moreover, we account for the economic inequalities resulting from residual and avoided climate impacts. We find that price-based climate policies without compensatory measures increase economic inequality in most countries and across models. However, revenue redistribution through equal per-capita transfers can offset this effect, leading to on average decrease in the Gini index by almost two points. When climate benefits are included, inequality is further reduced, but only in the long term. Around mid-century, the combination of dried-up carbon revenues and yet limited climate benefits leads to higher inequality under the Paris target than in the Reference scenario, indicating the need for further policy measures in the medium term.