The Eocene-Oligocene transition (EOT) represents a period of global environmental changes particularly marked in Europe and coincides with a dramatic biotic turnover. Here, using an exceptional fossil preservation, we document and analyse the diversity dynamics of a mammal clade, Cainotherioidea (Artiodactyla), that survived the EOT and radiated rapidly immediately after. We infer their diversification history from Quercy Konzentrat-Lagerstätte (South-West France) at the species level using Bayesian birth-death models. We show that cainotherioid diversity fluctuated through time, with extinction events at the EOT and in the late Oligocene, and a major speciation burst in the early Oligocene. The latter is in line with our finding that cainotherioids had a high morphological adaptability following environmental changes throughout the EOT, which likely played a key role in the survival and evolutionary success of this clade in the aftermath. Speciation is positively associated with temperature and continental fragmentation in a time-continuous way, while extinction seems to synchronize with environmental change in a punctuated way. Within-clade interactions negatively affected the cainotherioid diversification, while inter-clade competition might explain their final decline during the late Oligocene. Our results provide a detailed dynamic picture of the evolutionary history of a mammal clade in a context of global change.