Environmental change can create opportunities for increased rates of lineage diversification, but continued species accumulation has been hypothesized to lead to slowdowns via competitive exclusion and niche partitioning. Such density-dependent models imply tight linkages between diversification and trait evolution, but there are plausible alternative models. Little is known about the association between diversification and key ecological and phenotypic traits at broad phylogenetic and spatial scales. Do trait evolutionary rates coincide with rates of diversification, are there lags among these rates, or is diversification niche-neutral? To address these questions, we combine a deeply sampled phylogeny for a major flowering plant clade-Saxifragales-with phenotype and niche data to examine temporal patterns of evolutionary rates. The considerable phenotypic and habitat diversity of Saxifragales is greatest in temperate biomes. Global expansion of these habitats since the mid-Miocene provided ecological opportunities that, with density-dependent adaptive radiation, should result in simultaneous rate increases for diversification, niche, and phenotype, followed by decreases with habitat saturation. Instead, these rates have significantly different timings, with increases in diversification occurring at the mid-Miocene Climatic Optimum (~15 mya), followed by increases in niche and phenotypic evolutionary rates by ~5 mya; all rates increase exponentially to the present. We attribute this surprising lack of temporal coincidence to initial niche-neutral diversification followed by ecological and phenotypic divergence coincident with more extreme cold and dry habitats that proliferated into the Pleistocene. A lack of density-dependence contrasts with investigations of other cosmopolitan lineages, suggesting alternative patterns may be common in the diversification of temperate lineages.