Only over a long time will there be a measurable increase in surface temperature. (realclimate.org)
The reason I asked what was your model, was because it appears your broad model assumes linear increase in CO2 means near linear increase in surface temperature. (skepticalscience.com)
(Note: a 20 °C increase in surface temperatures does not directly translate to a large increase in air temperatures. (earthobservatory.nasa.gov)