It's also worth noting that the phenomenon is hardly a secret. It's been discussed at length in the scientific literature for at least 15 years — basically, since scientists first recognized it. Here's a 1995 article from the journal Science, one of many.
It's also discussed in Chapter 6 of the Intergovernmental Panel on Climate Change's most recent report, pages 472-473.
So why does divergence happen? First, divergence doesn't happen in all tree-ring records. In some, trees respond positively to warming temperatures just as scientists would have predicted. Generally, scientists find that the divergence phenomenon shows up in trees from the far northern hemisphere, but not the southern, although that may be due to a paucity of samples from the southern hemisphere.
Even in the northern hemisphere, some tree rings don't show divergence.
Where they do diverge, one crucial factor seems to be the micro environment of the sampled tree. If temperatures are rising there, but moisture isn't, then higher temperatures lead to water stress, which retards, rather than enhances, growth.
In an e-mail, Rosanne D'Arrigo, senior research scientist at the Tree-Ring Lab at Columbia University's Lamont-Doherty Earth Observatory, explains: "[B]eyond a certain threshold level of temperature the trees may become more stressed physiologically, especially if moisture availability does not increase at the same time."