The Palaeocene-Eocene Thermal Maximum (PETM) was a significant global warming event in Earth's deep past (56 Mya). The warming across the PETM boundary was driven by a rapid rise in greenhouse gases. The event also coincided with a time of maximum insolation in Northern Hemisphere summer. There is increased evidence that the mean warming was accompanied by enhanced seasonality and/or extremes in precipitation (and flooding) and drought. A high horizontal resolution (50 km) global climate model is used to explore changes in the seasonal cycle of surface temperature, precipitation, evaporation minus precipitation and river run-off for regions where proxy data are available. Comparison for the regions indicates the model accurately simulates the observed changes in these climatic characteristics with North American interior warming and drying, and warming and increased river run-off at other regions. The addition of maximum insolation in Northern Hemisphere summer leads to a drier North America, but wetter conditions at most other locations. Long-range transport of atmospheric moisture plays a critical role in explaining regional changes in the water cycle. Such high-frequency variations in precipitation might also help explain discrepancies or misinterpretation of some climate proxies from the same locations, especially where sampling is coarse, i.e. at or greater than the frequency of precession.This article is part of a discussion meeting issue 'Hyperthermals: rapid and extreme global warming in our geological past'.