The warmer regions harbor more species, attributable to accelerated speciation and increased ecological opportunities for coexistence. While correlations between temperature and energy availability and habitat area have been suggested as major drivers of these biodiversity patterns, temperature can theoretically also have direct effects on the evolution of diversity. Here we experimentally studied the evolution of diversity in a model adaptive radiation of the bacterium Pseudomonas fluorescens across a temperature gradient. Diversification increased at higher temperatures, driven by both faster generation of genetic variation and stronger diversifying selection. Specifically, low temperatures could limit the generation of diversity, suggested by the observation that supply of genetic variation through immigration increased diversity at low, but not high temperatures. The two major determinants of mutation supply, population size and mutation rate, both showed a positive temperature dependence. Stronger diversifying selection in warmer environments was suggested by promoted coexistence, and further explicitly inferred by the ability of evolved phenotypes to invade the ancestral type from rare. We discussed possible physiological and environmental mechanisms underlying the findings, most of which are likely to be general.