Last year (2012) a student, Derrek Wilson, and I published an article in the American Journal of Physics that contained a relatively straightforward calculation (for physicists, or other people with similar technical skills) of the warming effect of atmospheric CO2 under a number of simplifying assumptions: uniform surface temperature, no feedbacks, and neglecting the overlap with the absorption bands of other greenhouse gases.
The direct link to the paper's abstract is D. J. Wilson and J. Gea-Banacloche, Am. J. Phys. 80, 306 (2012).
For people who do not have a subscription to the American Journal of Physics, I am providing here a copy of the manuscript (which I am allowed to do according to their web posting guides).
Please note that the paper is copyright 2012 American Association of Physics Teachers. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Association of Physics Teachers.