I find HS's theory credible.
Here are some excerpts.
Low-level clouds cover more than a quarter of the Earth and exert a strong cooling effect at the surface. (For clouds at higher altitudes there is a complicated trade-off between cooling and warming.) The 2% change in low cloud during a solar cycle, as seen in figure 3, will vary the input of heat to the Earth's surface by an average of about 1.2 W m-2, which is not trivial. It can be compared, for example, with 1.4 W m-2attributed by the Intergovernmental Panel on Climate Change for the greenhouse effect of all of the additional carbon dioxide in the air since the Industrial Revolution (Houghton et al. 2001).
If cosmic-ray counts merely went up and down with the 11-year cycle of solar activity, there would be no trend in the climate. Systematic records of influx to the Earth's surface go back to 1937. Cosmic-ray changes before then can be seen in the rate of formation of radioactive isotopes such as beryllium-10, or inferred from the Sun's open coronal magnetic field. As seen in figure 5, the various methods agree that there was a pronounced reduction in cosmic rays in the 20th century, such that the maximal fluxes towards the end of the century were similar to the minima seen around 1900. This was in keeping with the discovery that the Sun's coronal magnetic field doubled in strength during the 20th century (Lockwood et al. 1999).
Here is prima facie evidence for suspecting that much of the warming of the world during the 20th century was due to a reduction in cosmic rays and in low-cloud cover. But distinguishing between coincidence and causal action has always been a problem in climate science. The case for anthropogenic climate change during the 20th century rests primarily on the fact that concentrations of carbon dioxide and other greenhouse gases increased and so did global temperatures. Attempts to show that certain details in the climatic record confirm the greenhouse forcing (e.g. Mitchel et al. 2001) have been less than conclusive. By contrast, the hypothesis that changes in cloudiness obedient to cosmic rays help to force climate change predicts a distinctive signal that is in fact very easily observed, as an exception that proves the rule.