The Paleocene and Eocene epochs provide examples of oceanographic conditions when the Earth had a stable climate much warmer than that of the modern world. Lower Cenozoic sediments thus provide a way to investigate how oceanographic processes might respond to extreme warming. Because high-latitude sea surface temperatures were significantly warmer during the early Cenozoic while tropical sea surface temperatures were similar to or somewhat less than modern, there may have been a much higher poleward oceanic heat transport at that time <Shackleton and Boersma, 1981; Barron, 1987; Sloan et al. 1995>. Here I develop a simple ocean thermohaline model to demonstrate that poleward oceanic heat transport could strongly warm the polar regions only if the strength of vertical mixing (vertical eddy diffusion) in the oceans is sensitive to changes in oceanic density structure. If this is true, the early Cenozoic oceans, because they had significantly less density stratification, could have had a thermohaline circulation as much as 3 times as strong as that of the modern ocean despite reduced temperature gradients. The model also predicts that an optimum bottom water temperature exists for maximum poleward heat transport: continued warming of the Earth does not continue to increase oceanic heat transport to the poles. The hypothesized sensitivity of oceanic vertical mixing to the density gradient should provide a positive feedback to both the transition to ice ages and to a future transition out of them. A test of the sensitivity of vertical eddy diffusion to density gradients can be studied through map and depth transects. In the horizontal direction, high vertical diffusion would be marked by relatively strong bottom water temperature gradients away from bottom water source regions. In the vertical direction, high vertical diffusion should be indicated by very small temperature gradients.¿ 1997 American Geophysical Union