The phrase "stratospheric cooling" refers to a decrease in temperature in the upper layer of Earth's atmosphere called the stratosphere. Full definition
The IPCC actually cites measurements of stratospheric cooling as evidence against the hypothesis that global warming would be caused by increased solar activity, as in such case the entire atmosphere would have to show a warming trend, including the stratosphere. (bitsofscience.org)
To elaborate on my comment # 3 above, the mechanism for stratospheric cooling consequent to increased atmospheric CO2 appears to be one of the most misunderstood elements of the greenhouse effect. (realclimate.org)
In regards to Michael Jankowski's comment (# 11), the Fu et al. (2004, Nature) article showed that the satellite record of tropospheric temperature trends, based on the Microwave Sounding Unit channel 2, is contaminated by stratospheric cooling on the order of -0.08 K / decade. (realclimate.org)