The onset of the Palaeocene/Eocene thermal maximum (about 55 Myr ago) was marked by global surface temperatures warming by 5-7 degrees C over approximately 30,000 yr (ref. 1), probably because of enhanced mantle outgassing and the pulsed release of approximately 1,500 gigatonnes of methane carbon from decomposing gas-hydrate reservoirs. The aftermath of this rapid, intense and global warming event may be the best example in the geological record of the response of the Earth to high atmospheric carbon dioxide concentrations and high temperatures. This response has been suggested to include an intensified flux of organic carbon from the ocean surface to the deep ocean and its subsequent burial through biogeochemical feedback mechanisms. Here we present firm evidence for this view from two ocean drilling cores, which record the largest accumulation rates of biogenic barium--indicative of export palaeoproductivity--at times of maximum global temperatures and peak excursion values of delta13C. The unusually rapid return of delta13C to values similar to those before the methane release and the apparent coupling of the accumulation rates of biogenic barium to temperature, suggests that the enhanced deposition of organic matter to the deep sea may have efficiently cooled this greenhouse climate by the rapid removal of excess carbon dioxide from the atmosphere.