The equation neglects feedback. Increased temps increase water vapor, another greenhouse gas.
Best estimate is 2.5 degrees. Yours was low estimate, mine was high.
The new formula gives 3.71Wm-2 for doubling carbon dioxide; 15% less than the previous formula. It is also below the mean of 4.0Wm-2 of the models (Cess 1993).
Reduced Greenhouse Warming
"The replacement of the previous formula (1) for calculating radiative forcing from carbon dioxide concentrations by the revised, more accurate formula (3), means that all existing and previous estimates for future temperature rise due to the greenhouse effect, should be reduced by 15%. In particular, the "temperature climate sensitivity" (temperature change for doubling carbon dioxide) figures of 2.5°C "Best Estimate", 4.5°C "High Estimate" and 1.5°C "Low Estimate" which are the basis for most IPCC projections, should be revised to 2.1°C, 3.8°C and 1.3°C respectively.
http://www.john-daly.com/bull-121.htm
Deal with the 2.5, AGW advocate!