Body size is a common focus of macroevolutionary, macroecological and palaeontological investigations. Here, we document body-size evolution in 19 species-level ostracod lineages from the deep Indian Ocean (Deep Sea Drilling Program Site 253) over the past 40 myr. Body-size trajectories vary across taxa and time intervals, but most lineages
(16 ⁄ 19) show net gains in body size. Because many modern ostracod taxa are larger in colder parts of their geographical
range, we compared the timing and magnitude of these size changes to established Cenozoic deep-water cooling patterns confirmed through δ¹⁸O measurements of benthic foraminifera in the samples studied. These data show a significant negative correlation between size changes and temperature changes (ostracods get larger as temperatures get colder), and that systematic size increases only occur during intervals of sustained cooling. In addition, statistical support for an explicit temperature-tracking model exceeds that of purely directional evolution. We argue that this Cope’s Rule pattern is driven by secular changes in the environment, rather than any universal or intrinsic advantages to larger body sizes, and we note some difficulties in the attempts to link Cope’s Rule to observations made within a single generation.