According to the data presented, over the last three decades, the period over which the curves appear highly correlated, solar irradiance has increased by a proportional factor of 0.0003.

The Earth's mean temperature anomaly by itself means nothing, it depends on how you define the earth's mean temperature in the first place, and that is a very subjective process (mean atmospheric temperature, air temperature at the surface, ocean water temperature at a depth of ten meters?---you take your pick!) Let's be generous and pick a round reasonable number of 273 degrees Kelvin, the freezing point of water. The temperature anomaly then translates to a proportional temperature variation of 0.002.

UV flux has increased by a proportional factor of .0001.

During that time, Neptune's bolometric magnitude has dropped (=gotten brighter) by 0.15 magnitude. But magnitude is based on a logarithmic scale, this corresponds to a proportional increase in total luminosity (bolometric means "at all wavelenghts") by the planet of roughly 15 per cent! Obviously, something is wrong here. I assume all corrections for orbital geometry, inverse square law and so on have been made, so either Neptune has a colossal greenhouse effect, or there is some kind of convective process heating up some layer of the atmosphere that contributes enormously to the temperature photometry. If the sun is indeed getting brighter, then you would expect sunlight reflected by the planet would get brighter by the same amount, the excess must come from some internal process on the planet.

I didn't feel like shelling out the $9 for the original article either, but what I see so far leads me to believe that the vertical scales of these graphs have been deliberately selected to make a point. If solar output increases of course there will be a vague general correlation of these properties, but the striking similarity of these curves looks suspicious to me.