What was done
The authors present a detailed 3000-year temperature reconstruction for South Africa, which they derived from a correlation between color variations in the annual growth layers of a stalagmite and an area-averaged regional temperature series.

What was learned
Several warm and cold periods were noted throughout the record.  The most pronounced cold period occurred during the Little Ice Age between AD 1500 and 1800, when temperatures were estimated to be about 1°C colder than they are presently.  Dramatic warming was experienced during the Medieval Warm Period at around AD 900, when temperatures reached 2.5°C higher than at present.  Another exceptionally warm period was noted in the late fifteenth century, when temperatures rose more than 3°C above the current level.  As for the late nineteenth century warming present in the instrumental surface record, the authors find "little evidence" of such a warming in the stalagmite temperature reconstruction.

What it means
There can be little doubt about the existence of both the Medieval Warm Period and Little Ice Age in South Africa.  Furthermore, there can be little doubt that the temperature excursions of these intervals were the result of natural climate variability.  As for why the recent rise in temperature observed in a nearby network of surface weather stations does not appear in the stalagmite record, we can only speculate it may be due to the surface temperature network being artificially influenced by the effects of urbanization, whereas the cave that is home to the stalagmite is not.