In addition to these shorter 11-year solar sun-spot cycles, there are longer cycles where there have been prolonged periods with weaker solar maximums and longer solar minimums with no sun spots at all.
This last solar minimum exhibited almost 3 years without a sun spot. Now that we are finally entering into a solar maximum, the sun only has half as many sun spots as it would during other maximums. Only time will tell if this weaker solar pattern will continue.
Okay, so what happens with Earth temperatures and climate when the sun goes through these prolonged solar minimum's? Well, the last time it happened in the 1600-1800's. This climatic period is known as the "Maunder Minimum" and "Dalton Minimum". What happened with the climate was that global temperatures were much colder than usual. This period, also calked "The Little Ice Age", resulted in cold winters where the Mississippi River, and Thames River in London routinely froze over each winter.
The interesting detail to this would be that in addition to colder global temperatures that occur during prolonged solar minima, is the possibility for increase seismic activity, Earthquakes and Volcanism. However, the mechanism between solar activity and vulcanism is still unknown. Some scientific prognosticators are predicting a possible increase in seismic and volcanic activity if a prolonged solar minimum occurs.
What is known is that higher solar wind is inversely correlated with cosmic rays. Instead of being hit by a stream of protons and electrons from the sun, when the solar wind is weak, greater amounts of high energy cosmic rays coming from interstellar space shower down on the Earth. Higher cosmic rays have been associated with higher cloud cover. Higher cloud cover traps more heat. Water vapor in clouds traps much more heat via the greenhouse effect than carbon dioxide.