Wolfram Alpha:

```The Keeling Curve
-----------------

Click on the following link to get the current
amount of CO2 in the atmosphere at the Mauna Loa
observatory in Hawaii.  The amount of CO2 in the
atmosphere is a factor in determining the temperature
of our planet.

Keeling Curve for Atmospheric CO2

Relationship Between CO2 Levels and Temperature
-----------------------------------------------

dT = ΛdF

Where,

Λ is the climate sensitivity.

- energy radiated back to space.  (W/m2)

and dT is the change in temperature (° C)

Empirically it has been found that:

dF = 5.38ln(C/C0))

Where C0 is the pre-industrial level of CO2 ~
280 ppm.

Studies have given a possible range of values
of 2 - 4.5° C warming for a doubling of CO2.  If
we assume an average of 3° C then:

Λ = 3/5.38ln(2))

= 0.87 C/W/m2

Plugging this back into our original formula gives:

dT =  0.87 * 5.38 * ln(410/280))

=   0.87 5.38 .38

= 1.78° C

Of course, this model is overly simplistic since
there are many other factors impacting temperature.
For example, the role of the oceans, the amount
of ice cover, and the amount of water vapour in
the atmosphere are not accounted for.  In addtion,
there other greenhouse gases present in the atmosphere
such as Methane, which also possess heat trapping
properties.  Nonetheless, this 'back of the envelope
calculation' does give some insight into the link
between global temperatures and CO2 levels in the
atmosphere.
```