"Natural cycles!"
The sun's heating does vary with the regular, predictable orbital changes of the earth ("Milankovitch cycles"). We're in a slow cooling trend which began 6000 years ago.
"The sun!"
Here are measurements of the sun's radiation:
http://data.giss.nasa.gov/gistemp/2007/
In October Mike Lockwood of the UK's Rutherford Appleton Laboratory and Claus Froehlich of the World Radiation Center in Switzerland published a paper that concludes:
"Here we show that over the past 20 years, ALL the trends in the Sun that could have had an influence on the Earth's climate have been in the OPPOSITE DIRECTION to that required to explain the observed rise in global mean temperatures."
http://journals.royalsociety.org/content…
So why don't global temperatures follow the sun's influence? Something else must be a much stronger factor in the trend.
Observations of past orbital cycles ("natural cycles" of the sun's warming influence) show that the sun's direct influence exists, but that it cannot fully explain past climate change. There are other major, often stronger factors involved that affect the earth's retention of the heat that the sun delivers. One of those factors is the involvement of carbon-based gasses ("greenhouse gasses") which help the earth trap more of the heat from the sun. The existence of greenhouse gas warming is easily and dramatically demonstrated by the temperature of Venus, which has a much higher concentration of CO2 in its atmosphere.
So we know from measurements that the sun hasn't been increasing in strength for the past few decades, that its major recent trends have been negative, and that current climate trends haven't been following its minor changes in radiation. We can see the temperature on Venus due to greenhouse gases. We know that greenhouse gases on earth were elevated during "natural cycles" in the past that didn't coincide with the timing of the sun's influence.
The Earth's average surface temperature of 15 °C (59 °F) is about 33 °C (59 °F) warmer than it would be without the greenhouse effect.
http://en.wikipedia.org/wiki/Greenhouse_…
Here's how the greenhouse effect works:
"For the Earth's temperature to be in steady state so that the Earth does not rapidly heat or cool, this absorbed solar radiation must be very closely balanced by energy radiated back to space in the infrared wavelengths."
"The visible solar radiation mostly heats the surface, not the atmosphere, whereas most of the infrared radiation escaping to space is emitted from the upper atmosphere, not the surface. The infrared photons emitted by the surface are mostly absorbed in the atmosphere by greenhouse gases and clouds and do not escape directly to space."
Increase the greenhouse gasses, and you increase the heat trapped.
We've recently been able to measure the imbalance between the incoming and outgoing radiation:
Earth’s Energy Out of Balance: The Smoking Gun for Global Warming
http://www.columbia.edu/~jeh1/imbalance_…
"Scientists at Columbia University, NASA, and the Department of Energy have found that the Earth is out of energy balance: the Earth is absorbing more energy from sunlight than it is emitting back to space in the form of heat radiation. This imbalance provides confirmation of global warming theory and a measure of the net forcing that human’s are applying to the Earth by adding greenhouse gases and other pollutants to the Earth’s atmosphere."
Increased radiation from the sun could make the earth warmer, but in a steady state the warmer earth would simply radiate more heat back to space. The key here is the imbalance. Heat is being trapped. The earth is warming. Greenhouse gasses in the atmosphere provide the heat-trapping mechanism, but if they were steady the outgoing radiation would match the sun's radiation. What NASA is saying is that the increase in greenhouse gasses provides the current unbalanced state between the earth's incoming and outgoing energy.
So the sun's influence can be debated (credible papers put its influence as negative), but the measured lack of matching heat radiation means that more of the sun's energy is being trapped, and we know that mechanism to be greenhouse gasses.