The theory goes as follows:
1. Earth is 33 degrees warmer than it should be based in incoming solar radiation alone;
2. This is due to 'greenhouse gases' and 'trapped radiation';
3. Hence more greenhouse gases = higher temperatures.
Item 1. is the most outrageous Diagonal Comparison of all time. If this is not a valid comparison, then we need not concern ourselves with whether 2 and 3 are valid*.
The Hansen approach is to calculate the Effective Temperature** of Earth by adjusting incoming solar radiation down for the high average albedo of clouds to arrive at a low average expected temperature - and then comparing that with the actual higher temperature of land or ocean surface and completely ignoring the actual lower temperatures of clouds.
A proper scientific comparison compares like with like. So if you calculate the Effective Temperature based on the average albedo of clouds, land and oceans, you have to compare it with the overall average temperature of cloud tops, land and ocean surface... and you end up with a 'Greenhouse Effect' of +/- zero, zilch, nothing. Here are the numbers. (Cloud top altitude in pale blue as that is my best estimate and the variable most worthy of research or debate).
It all matches up nicely. Actual temperature ≈ expected temperature and outgoing infrared radiation ≈ incoming solar radiation:
BBC - A brief history of the Earth's CO2
Wikipedia - effective temperature
How high in the sky are clouds?
Scientists detect world's coldest cloud hovering over Pacific Ocean
What is Earth’s surface emissivity?
* The real explanation for the apparent 33 degree difference is far simpler; and the most plausible reason for the recent slight increase in temperatures is Ozone Depletion, but these have been crowded out. Whether you understand or agree with these is irrelevant to the question of whether there is any evidence for 'greenhouse gases' causing 33 degrees of warming in the first place.
** Effective Temperature is the hypothetical temperature that a planet would have to be to emit as much radiation as it receives from its star, assuming 100% emissivity. But it is a good first approximation for the actual temperature for a fast-spinning planning planet with a thick atmosphere, like Earth.
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The other Diagonal Comparison is that the official average surface temperature is overstated by about 33 degrees because it is weighted towards very low altitudes, which inevitably show a higher average temperatures than if Earth were covered with mountains. I'll cover that in Part 2, and then I'm done with this nonsense.