What was done
The authors studied the ¹⁸O/¹⁶O profile through a stalagmite from a cave in New Zealand, which was dated by the ¹⁴C method.

What was learned
The proxy temperature record provided by the stalagmite was broadly similar to the climate record of England, exhibiting a period in the early part of the past millennium that was about 0.75°C warmer than it was in the mid-20th-century.  In addition, the temperature near the latter part of the 17th century was about 0.75°C cooler than it was in the middle of the 20th century.

What it means
The authors state that one of their objectives was to compare the temperature record from New Zealand - which they emphasize is "in the Southern Hemisphere and a region meteorologically unrelated to Europe" - with the English climate curve.  Their conclusion?  "The temperature curve for New Zealand is apparently broadly similar to England and such climatic fluctuations as the Medieval Warm Period and Little Ice Age are not just a local European phenomenon," which conclusion is totally at odds with the recent attempt of climate extremists to relegate these major climatic episodes to a small region around the north Atlantic Ocean.