Solar radiance is without argument the greatest contributor to Earth's heat budget. However, the sun's variability is probably not significant enough in the scale we're discussing to account for the level of change we've seen. In fact, oceans with their high heat capacity have no doubt moderated temperatures to an unappreciated degree. But that high heat capacity only makes the atmospheric component more important; if there were to a be the chemical equivalent of a phase change or CO2 saturation in the oceans, we're screwed.
{However, the sun's variability is probably not significant enough in the scale we're discussing to account for the level of change we've seen.}
So you would dispute the NASA data which has also evidenced planet warming comparable with solar output, on Mercury, Venus, Mars, Jupiter, and Saturn?
Again, most climatologists now agree that the warming period stopped in 2002, strangely enough when solar output declined.
CO2 saturation in the oceans is impossible, given the moderating influence of ocean flora. As I study ice core CO2, overlaid with other tempature indicators, CO2 is a lagging climate indicator, not a predictor.