'Hyperthermals' are intervals of rapid, pronounced global warming known from six episodes within the Palaeocene and Eocene epochs (similar to 65-34 million years (Myr) ago)(1-13). The most extreme hyperthermal was the 170 thousand year (kyr) interval(2) of 5-7 degrees C global warming(3) during the Palaeocene-Eocene Thermal Maximum (PETM, 56 Myr ago). The PETM is widely attributed to massive release of greenhouse gases from buried sedimentary carbon reservoirs(1,3,6,11,14-17), and other, comparatively modest, hyperthermals have also been linked to the release of sedimentary carbon(3,6,11,16,17). Here we show, using new 2.4-Myr-long Eocene deep ocean records, that the comparatively modest hyperthermals are much more numerous than previously documented, paced by the eccentricity of Earth's orbit and have shorter durations (40 kyr) and more rapid recovery phases than the PETM. These findings point to the operation of fundamentally different forcing and feedback mechanisms than for the PETM, involving redistribution of carbon among Earth's readily exchangeable surface reservoirs rather than carbon exhumation from, and subsequent burial back into, the sedimentary reservoir. Specifically, we interpret our records to indicate repeated, large-scale releases of dissolved organic carbon (at least 1,600 giga-tonnes) from the ocean by ventilation (strengthened oxidation) of the ocean interior. The rapid recovery of the carbon cycle following each Eocene hyperthermal strongly suggests that carbon was re-sequestered by the ocean, rather than the much slower process of silicate rock weathering proposed for the PETM(1,3). Our findings suggest that these pronounced climate warming events were driven not by repeated releases of carbon from buried sedimentary sources(3,6,11,16,17), but, rather, by patterns of surficial carbon redistribution familiar from younger intervals of Earth history.