47 terawatts of heat are conducted from below to the surface, but the rate of conductivity is low enough that the effect is ignored for most applications. Advocates of AGW ignore heat conduction in the crust and talk only about the heating of the atmosphere and oceans.
What's amazing though is that there's so much money funding so many studies of the heating of the atmosphere&oceans, but nobody wants to say what the average temp is. A hundred million miles away everyone agrees that the surface of the sun is exactly 5,778K, but right here at home everyone's close-lipped about the temp of the earth's surface.
You have a point, but I suspect you don't give the anthropogenic effect it's due merit. I strongly disagree that CO2 is the primary effect of our warming.
We have capped off parts of our globe with buildings, concrete, and asphalt changing the emissivity of that land area. Worse yet, the rainwater no longer causes the same hydrological cycle in such regions. When such rainwater is mostly now channeled into storm sewers, we lose evapotranspiration, which is very significant. As city areas grow, very few meteorological stations are immune to the effects of urban and rural increases in temperature.
We have polluted the skies with aerosols, and enough cover the ice regions to reduce the albedo. A reduction of 1% in ice albedo causes more melting than quadrupling CO2 in the atmosphere, even with the warming claimed for CO2, and we have reduced the albedo far more than 1%.
We have had a significant effect on the earth, only not because of CO2.
Then there is the sun. It takes around 100 years for the solar, ocean, atmospheric coupling to equalize to 70%. The solar radiance peaked in 1958, and it is around this time-frame that we finally see the end of warming by the sun.
You would be wise to not dismiss our changes of the earth, and keep the truth in perspective.
There are probably $200 spent to show AGW for ever $1 spent to not show it in the climate sciences. That's what happens when politics controls science.