In this dose of skeptical peer-reviewed [see some debate about the adjective in the comments] literature about the climate, we look to Energy and Environment. In the August 2008 issue, David Douglass and John Christy have the following article:
The tropical temperatures are nicely described by a linear function of the ElNino/LaNina (ENSO) region-3.4 index: the correlation is very strong. They determine the two coefficients (linear and absolute) and subtract this ENSO contribution from the original temperature anomaly. The remainder is not visibly correlated with CO2 - wrong fingerprints - and it apparently comes from additional effects in the extratropics.
Nevertheless, whatever the origin is, they can extract the underlying linear trend and it is currently 0.6 +- 0.1 °C per century (from the 1979-2008 data). This matches the normal greenhouse calculation without any feedback i.e. the climate sensitivity close to 1 °C. There could exist positive feedbacks but they would have to be canceled by negative forcings to match the data.
They use a paper by Chýlek (2007) to argue that the aerosols are too small to influence the tropical temperature enough. They also think that the negative forcings can't have a solar origin: with these beliefs, they can formulate their finding as an upper bound on the climate sensitivity. Qualitatively speaking, there exists no known cooling mechanism that could explain the cooling between 1998 and 2008 - that remains essentially flat even if the ENSO index is subtracted. Note that the IPCC would imply up to 0.45 °C of CO2-induced warming in this decade which can be pretty much falsified.
These calculations seem to imply that the total feedbacks are essentially zero and, assuming that the trend comes from carbon dioxide, the CO2 climate sensitivity is close to 1 °C, as can also be determined in other ways (see e.g. Schwartz). In other words, one should conclude that the CO2-induced warming in the 21st century will be close to 0.6 °C, the same centennial trend that they extracted by their analysis. This signal is smaller than the effect of an ordinary El Nino or La Nina.
Hat tip: Roger Pielke Sr and Anthony Watts
An unrelated climate link to the New York Times: Permafrost will remain frozen even if there's global warming.