I like the answers provided by Dave H and Climate Realist. Dave H's choice of the South Pole is indeed a cherry picked location where the normal climate drivers act some what differently.
- Ocean Currents: The South Pole is some what isolated from the rest of the world's ocean currents not just by the land mass, but also by the Antarctic Circumpolar and Subpolar currents. http://en.wikipedia.org/wiki/File:Corrientes-oceanicas.gif
Thus, much of the signal provided by the AO, IO, PO, ENSO and other ocean current based oscillations with periods between a few months http://en.wikipedia.org/wiki/ENSO
to over a thousand years http://en.wikipedia.org/wiki/Thermohaline_circulation
have less effect on the South Pole than any other part of Earth.
- Wind Currents: The winds are moving away from the South Pole. http://i.imwx.com/web/multimedia/images/blog/antarctica_wind_pattern.jpg
Thus, the air coming to the South Pole come from high altitude. There is very little moisture there.
- Solar: The South Pole is still subject to changes in the solar output. http://en.wikipedia.org/wiki/Sun_Spots
However, this only applies to the Antarctic "Summer" from September to March.
Thus, the physics are a little different for the South Pole in that the signal to noise ratio http://en.wikipedia.org/wiki/Signal-to-noise_ratio
for the effect of atmospheric CO2 in the greenhouse effect would be expected to be higher there, than anywhere else on Earth.
I calculated the answer myself, and came up with about 1 kelvin as Climate Realist suggested, provided that I used the maximum numbers available for the likely effects. Half that amount is also reasonable. That calculation was solely based on the shoulders of the saturated peaks in the infrared range for CO2 (12 micron). I completely ignored the unsaturated peaks in the visible range (2 micron) where the greenhouse effect is negative. I suspect that Climate Realist's data comes from someone who did the calculation the same way I did. Examine the absorption spectrum for CO2 and its levels of saturation and see for yourself whether it appears that CO2 is going to have a greenhouse effect or an anti greenhouse effect. I cannot tell from looking at the data. http://en.wikipedia.org/wiki/File:Atmospheric_Transmission.png
When I include the anti-greenhouse effect of CO2 zero is a legitimate estimate for the effect.
Greenhouse Effect (11 - 21 microns) ~= Anti-Greenhouse Effect(1.8 - 2.2 microns)
Net Greenhouse Effect ~= 0
for additional CO2 to the 390 ppmv there now.