Geological and paleontological records demonstrate that Earth's long-term ocean paleotemperature trend over the Cenozoic has been broadly downward, transitioning from extreme early warmth into modern ice-house conditions.
The claim addresses the long-term ocean paleotemperature trend, which is a specific, empirically testable geologic hypothesis. Multiple papers (specifically [0], [6], and [8]) discuss the Cenozoic cooling trend from early Eocene hothouse conditions to later icehouse and colder modern climates. None of the retrieved papers refute this overarching downward trend, leading to a verdict of SUPPORTED.