Why is the ocean paleotemperature trend downwards?
I recommend you read the original paper Lear et al. (2000). In it they explain that the results are controlled by processes in polar regions and likely associated with the polar surface temperature. The surface temperature will vary considerable depending on the proximity and extend of the deep water formation areas. As these areas are fairly local, relatively small changes in the location and extend of deep water formation can result in deep water temperature being altered. The uncertainty associated with using single cores to estimate global temperatures is thus quite large. What the authors suggest is a predominantly ice-free world during most of the Paleocene and Cretaceous periods and several ice-sheet expansion events during the Oligocene, Miocene and Pleistocene. If there is no ice, the polar and sub-polar deep-water formation is limited and the water temperatures in the deeper part of the ocean is much warmer.

The temperature record shows a general cooling trend for the past 50 My, but its resolution is too low to define abrupt temperature extremes. Assuming that the process of deep water formation at high latitudes prevailed throughout the past 50 My, these deep-ocean temperatures can be inferred to represent polar surface temperatures (1). The temperature trend (Fig. 1C) appears to comprise four main cooling phases separated by periods of more stable temperatures. These cooling phases occur during the early Middle Eocene, the Late Eocene through Early Oligocene, the late Middle Miocene, and the Plio-Pleistocene.
Alternative evidence supports the existence of these principal cooling phases. A sharp cooling in the early Middle Eocene has been invoked to explain the abundance of siliceous sediments of this age (20). The Early Eocene warm climate is thought to have promoted in- tense chemical weathering of siliceous rocks at
high latitudes, which resulted in high concentrations of dissolved silica in the oceans. The subsequent cooling stimulated upwelling of nutrient-rich water and intense biosilicification. The cooling over the Late Eocene through Ear- ly Oligocene is coincident with the transition from “Paleogene” to “transitional” benthic foraminiferal faunas and high extinction rates in planktonic and terrestrial faunas. The initiation of this deep water cooling also coincides with a reduction in the extent of tropical rainforests on land (21, 22). The cooling in the late Middle Miocene is marked by a narrowing of tropical and warm subtropical biotic provinces in terrestrial and marine environments (23). Warmwater diatom assemblages were replaced by cold-water species at this time (24). The Plio-Pleistocene cooling is not represented by an extinction phase in benthic foraminiferal faunas; instead, faunal groups adapted to the changing bottom water conditions by migration (21).

When you use data from other regions, you get a much different result. For instance, Elderfield &amp; Ganssen (2000) showed how different the temperature changes can be for different species and locations. 
Their data are much more recent and suggest an increase in temperature over the last 20,000 years. As always, everything depends on the temporal scales. One issue that tends to be true is that estimates for periods long time ago tend to have larger uncertainties.