We suspect that sunspots do not affect global warming and there is no evidence that they do. The Maunder Minimum ( in sunspot activity ) does coincides with the middle and coldest part of the Little Ice Age ( see Wikipedia on LIA ). But we know that the solar output during sunspot active regions vs sunspot inactive times is a difference of less than one tenth of one percent. This is statistically insignificant and scientists do not consider it a cause for the Little Ice Age.
Warming and cooling cycles are related to temperature variations on planets, but only in relation to the specific gas concentrations on those planets. Venus, Earth and Mars vary in many similar aspects, but not at the same time frame. This implies that the sun, which they all have in common, is not a primary factor for temperature variations.
While it may be true that sunspots do not directly affect Earth's temperatures enough to account for the recent period of global warming, there is an indirect effect that some researchers have verified.
Straight heat is not the only thing that the sun emits. There's a "solar wind" that is more active during periods of high sunspot activity. This solar wind "shields" (I put that in quotes because, in this case, the shielding is not such a good thing) the Earth from certain cosmic rays. These cosmic rays, when they enter our atmosphere, excite certain atmospheric molecules in such a way that they become more likely to be "seeds" for high-level cloud formation. These high-level clouds block sunlight from reaching the surface, thereby reducing temperatures. But when the sun is in a period of high sunspot activity, fewer of these cosmic rays get through, and fewer clouds form, and temperatures rise. We are in a period now of very low (zero, I believe) sunspot activity. So more cosmic rays are getting through, and more high-level clouds forming.
Very little. A number of independent measurements of solar activity which is strongly related to sunspot number indicates the sun has shown a slight cooling trend since 1960, over the same period that global temperatures have been warming. Over the last 35 years of global warming, sun and climate have been moving in opposite directions. An analysis of solar trends concluded that the sun has actually contributed a slight cooling influence in recent decades.
It has been speculated that solar activity could also be related to cosmic rays and subsequently to cloud cover and temperature, the same applies, and this is addressed in my previous answer. All these solar phenomena have been decreasing whilst temperature has been increasing from around 1975.
The intensity of solar radiation is highly correlated with sunspot numbers since both sets of measurements began. (see link solar cycle data). I have added this clarification.
Quote "It is shown that the contribution of solar variability to the temperature trend since 1987 is small and downward; the best estimate is −1.3% and the 2σ confidence level sets the uncertainty range of −0.7 to −1.9%. The result is the same if one quantifies the solar variation using galactic cosmic ray fluxes (for which the analysis can be extended back to 1953) or the most accurate total solar irradiance data composite" (Lockwood 2008).
2009 and 2010 were very inactive years for the sun, yet very high temperatures were recorded the last year being a record year by many criteria. The last decade was also the warmest on record.
From 1900 to the 1960s the sunspot count has been upward; from the 1960s to the present, it has diminished somewhat. The number of sunspots correlates with the intensity of solar flux since 1979, when satellite measurements became available.
In Conclusion, "while the sun contributed to warming in the early 20th Century, it has had little contribution (most likely negative) in the last few decades"
If you are still in any doubt, see the attached graph Temperature v Solar Activity.
It should be pointed out that the IPCC claims that the science behind solar variation and it's ability to cause temperature change on our planet are still "poorly understood". This means that anyone that says they have a good grasp on the subject or they know one way or another, is wrong. We simply do not know. There has always been a connection between sunspots and temp. but the evidence in either direction is not conclusive.