The Eocene is just before the earth went into a period of "icehouse" climate (that's still going on). During the part of the Eocene this article refers to, the earth was in a "greenhouse" phase, and global temperatures were much warmer than they've been any time since.
At that time (and throughout the majority of Earth's history), there likely weren't any significant ice caps on the planet.
On very long timescales, the Earth goes through periods of icehouse and greenhouse climates. We're currently in an "interglacial" within a period of icehouse climate that has persisted since the late Eocene. Most of Earth's history is dominated by long phases of greenhouse climate. During these, the global climate is more stable and much warmer. We don't have ice ages, and there probably aren't any ice caps at the poles.
The last period of icehouse climate began just after this, in the late Eocene. (Again, the "ice ages" you hear about are glacials and interglacials within a period of icehouse climate.)
Also, as other folks have mentioned, the Eocene is relatively recent, and Antarctica was essentially in its present-day position (the coals and other "warm-weather" rocks in Antarctica date from much earlier when it was near the equator).
Regardless, it is quite interesting that sea surface temperatures were as warm as this evidence shows! I just wanted to put this into a bit of perspective.
*Caveat to all of this: I'm a geologist and not a climatologist.
The other bit of information that I would really find useful as a lay person is how temperature distribution varied during the "greenhouse" climates. For example, was it linear to todays differential, implying that if I can directly apply an increase of 20C to today's temp and say that the avg. CA temp would be 34C from the 14C referenced currently or is it more even and the jump at extremes will be significantly larger or smaller than at equator?
Ocean circulation plays a large role in regional (and global) variations in climate. If nothing else, the changes in the shape of the ocean basins over time would result in very different regional climate patterns, even if the average global temperature stayed the same.
On top of that, changes in average global temperature tend to vary strongly by latitude, if I remember correctly.
Shouldn't we welcome this? Lost in the debate about climate change is the question of whether or not the earth would be better off much warmer. Obviously there are costs to such change, but there are clearly benefits.
A lot of earth's land is tied up in uninhabitable frigid places. The idea that we should not slow or even intentionally accelerate global warming is not a completely nonsensical one.
Yale promo: temperatures in parts of Antarctica reached as high as 17 degrees Celsius (63F) during the Eocene, with an average of 14 degrees Celsius (57F) — similar to the average annual temperature off the coast of California today.
PNAS abstract: Here, we present multiproxy data from Seymour Island, near the Antarctic Peninsula, that provides well-constrained evidence for annual SSTs of 10–17 °C (1σ SD) during the middle and late Eocene.
Come on, give me that bloody headline writing job already!!