If you were throwing billions and billions of tons of CO2 in the atmosphere knowing that CO2 does have some impact on the energy containment of the atmosphere you might suspect that you could measure the surface temperature and the temperature of the lower troposphere and "see" some impact that would let you know right off the bat how much damage you are doing.
Reynolds Optimally Interpolated SST is available on the KNMI Climate Explorer website along with the Remote Sensing Systems (RSS) Lower Troposphere data in actual temperatures. Reynolds in degrees C and RSS in degrees K which should mean that you can actually estimate energy based on the temperatures. Of course there are margins of error that should be considered, but just for grins let's ignore that for a moment. Above I have plotted the difference in the two data sets which is degrees C or K depending on you mood. After using a 27 month three layer cascade filter instead of removing the seasonal anomaly that is what I got. From 1995 to present the average difference varies 0.128C degrees. that is pretty impressive, but both are satellites one trying to measure the ocean surface skin layer and the other the "lower" troposphere which based on the average or environmental lapse rate would be 21.2/6.5=3.26 kilometers or just above the marine atmospheric boundary layer at 2.5 to 3 km depending on who you like to reference. The average temperature of the RSS version of the LT is just below zero C at 272.4K degrees and the 60S-60N SST average is 20.37 C degrees. The SST is whatever mask that Reynolds uses and the RSS is truly "global" including land and ocean areas according to KNMI.
The reason I dug out this data was for the Atmospheric R-value which I have posted on in the past. That R-Value is about 0.192 and is pretty much limited by the specific heat capacity of the atmosphere and the force of gravity. The atmosphere can't "store" energy in the normal sense. It can "gain" energy if the oceans warm and the rates of deep convection and polar advection stay pretty close to the same, but it is not just going to "store" energy. So the R-value I thought might be of some use until I notice how much imbalance there is between the hemispheres.
So this is the atmospheric R-Value between the Sea Surface and just a little above the MABL which I used in my estimates. It would be nice to have a much longer data set to play with, but using what we have I thought it would be fun to share.
UPDATE: In case you were wondering,
R-Value in case you were wondering is in K/Wm-2 which is the same as "sensitivity" since CO2 is basically just adding some resistance to an already resistive atmosphere. If you invert the R-value you have a U-value which is typically used for lower values. 1/0.237=4.2 Wm-2/K so if I add 3.7 Wm-2 or resistance/insulation then, 3.7/4.2=0.88 or the temperature differential should increase by 0.88K degrees. This however is for the actual surface to approximate atmospheric boundary layer (ABL) at ~3000 meters. That surface, the ABL is a new reference layer for a less moist atmosphere and the RSS data provides another reference temperature, ~0 C degrees, you just need another "surface" as a reference for the next atmospheric layer.