The increased solar flux is partially captured by our magnetic field, which partially shields us from incoming cosmic radiation, which has been absolutely demonstrated to be a significant cause of cloud formation. More solar flux equates to increasing atmospheric temperature, every 11 years.
The 11 year cycle can be seen in the cosmic ray flux, but not in the temperature curve, at least not with the unaided eye. Note that the cosmic ray theory predicts that with decreasing intensity, we would expect the temperature to rise. But we observe that the smoothed cosmic ray flux shows some wiggling, but no clear trend. So the cause for the rising temperature must be something else. The image is from this post on realclimate. Go there for more details about the cosmic ray theory.