Studies with poxy data have shown the sun to vary greatly over the last several centuries. The IPCC conveniently picks 1750 as their starting timeline to show industrialization has the effect they claim, when solar energy started increasing in 1713 after the maunder minima. During this time, if you take Lean et. al. 2000, and the supplemental 2005 additions, you find the sun has increased by 0.18% This is not talking a low to high solar cycle, but that much from the 11 year average. This is all backed up by other studies, though they have differing results. They all agree there are marked increases in the suns output. There is a growing consensus that the change is more like 0.24% as the sciences are more and more understood..
As your link correctly points out, even satellite data isn't certain because of instrument drift. The latest two SOURCE satellites with TIM and other equipment has the best calibrated equipment to date, and also has equipment seeing deeper into the shortwave spectrum. The trend from the start of satellite measurements shows a very marginal decrease.
Simply physics equations prove that a 0.18% increase in solar radiation gives a much larger increase of radiative forcing than the IPCC claims. The actual calculations are about 8 times larger for solar than the IPCC claims, because they only include the "direct forcing." They ignore the "indirect forcing."
The numbers have nothing to do with fusion, but more the magnetic changes in the sun. Scientists have noted short and long term cycles, and have predicted the solar output to be decreasing through at least the next two solar cycles, and some say we may enter a cooling as great as the maunder minima was.
As for the simple math of the sun. If we took at solar TSI vs. temperature and assign any number, I'll use 1360 W/m^2, to correspond to a global average of 15 Celsius, and increase the TSI by 0.18%...
15 C = 288.15 K
Watts to surface temperature is a fourth root/power of four function.
1.0018^0.25 = 1.00045
288.15 x 1.00045 = 288.28
288.28 = 273.15 = 15.13
15.13 - 15 = 0.13 degree increase, just for that 0.18% solar increase.
This is already 20% of what the IPCC is claiming for a temperature increase, but they claim the suns increase is only 7.2% of the radiative forcing increase (0.12/1.66 = 7.2%).
However, it isn't that simple to go from no atmosphere to an atmosphere. When the IPCC stops lying to us, I might start believing them.
This 0.18% conveniently equates to a 0.12 W/m^2 forcing, directly absorbed by the atmosphere. take a look at this:
This is an accepted earth energy budget at the time of the AR4. Please note that the sun is also partially reflected, and absorbed by the surface. Any increase in surface absorption will be proportionally reemitted as upward IR. The greenhouse effect will also be affected proportionally. Changes in greenhouse gas level are not linear, but the output is linear to the input of power. This simple graph shows the actual change of direct and indirect forcing to be 0.93 W.m^2. Not just the 0.12 W/m^2. When you compare that to the 1.6 W/m^2 claimed for forcing increases since 1750, you see it is 58% of the forcing change. The sun has the greatest influence.