To contemplate all the possible variables that affect the temperature of the atmosphere.

I agree with you that the solar energy output can fluctuate to certain degree, but I do not believe that it is the cause of the short term heat rise or the rapid fall in the air temperature that seems to happen occasionally.

As I understand it, the weather has a lot to do with pressure differences in the atmosphere.
In a similar manner, I believe that the total atmospheric pressure has a profound influence on the climate conditions of a planet, weather that planet is the Earth, Mars, Venus or some other planet.

If the pressure of the atmosphere on Earth was as low as it is on the moon the conditions here would be similar to the moon's.

Some information from a link you pointed to.

From:
http://en.wikipedia.org/wiki/Greenhouse_effect

The greenhouse gases
Water vapour is the single most important absorber (between 36% and 66% of the greenhouse effect), and together with clouds makes up between 66% and 85%. CO2 alone makes up between 9 and 26%, while the O3 and the other minor GHG absorbers consist of up to 7 and 8% of the effect, respectively.

There are two physics phenomenon that have been thoroughly investigated.
One is that; the warmer the liquid water is, the faster it evaporates.
The other one is that; the lower the gas pressure that presses against liquid water, the faster the water evaporates.
(The same effect works with any fluid. The Earth's atmosphere is a fluid.)

Now, if the two physics effects are combined on a global scale, so that the oceans become warmer than normal and the atmospheric pressure becomes lower than normal, then there will be more moisture than normal in the Earth's atmosphere, more moisture means greater greenhouse effect. Greater greenhouse effect means more heat retained by the atmosphere and so on, in other words a runaway greenhouse effect, like that on the planet Venus.

So, the question is: What effect in nature can cause such changes in the water and air? Or if you prefer, we can ask: Are such effects happening right now in the Earth's environment? I believe that they are.

It is evident from various studies that there has been temperature and perhaps pressure fluctuations in the Earth's atmosphere during the past centuries and eons, those fluctuations may have been caused by variations in the sun's energy output or the accumulation of the carbon dioxide in the atmosphere, but in today's studies, there seems to be no conclusive evidence that those effects, either individually or together, are causing the present temperature fluctuations.

What is causing the problem? I believe that it is mostly caused by an effect that has been totally ignored by the scientific community.
That effect being associated with the nuclear decay of the various fission byproducts that have been scattered into the atmosphere.