There are further errors in considering the solar cycle. One is that the variance in the UV portion of the solar irradiance spectrum is larger. It is 0.5 to 0.8%. The UV radiation interacts with the ozone in the stratosphere and the concentration of ozone varies with such effects as the solar cycle, volcanic emissions, ozone depleting substances, and climate change. Thus, the effect of the varying UV radiation on warming the Earth is further complicated by its interactions with the varying ozone levels.
Other important aspects of the solar cycle are the solar wind, which itself carries energy to the Earth and is part of the reason the ozone concentrations depend upon the solar cycle. Still another aspect of the solar cycle is that it causes the Sun's electromagnetic field to vary, especially during the more active parts of cycles, and to dump energy into the Earth through its interaction with the Earth's electromagnetic field.
Finally, the variations in the solar electromagnetic field with the solar cycle cause that field's shielding of the Earth from cosmic rays to vary. When the cosmic ray intensity increases, cloud cover increases and there is a net cooling effect upon the Earth as more sunlight is reflected back into space, except over Antarctica.
But, ignorance of these effects and the belief that all that matters is a supposed minuscule 0.1% variation of the visible light spectrum from the Sun has long puzzled our intrepid climate modelers, since there has been some countervailing observational evidence that the solar cycles somehow matter. Finally, a few climate modelers are attempting to introduce solar cycle issues into their computer models, even if only very partially. They have been astounded to find that there are significant effects! They still present these as smaller variations than those caused by man's emissions of CO2, but important if one is to understand climate change over periods of a couple of decades.
The recent work of Gerald Meehl and colleagues at the National Center for Atmospheric Research has begun to try to understand aspects of the solar cycle interaction with La Nina and El Nino and other effects upon the Pacific Ocean and trade winds. You can read about this work at Science Daily.