Fair enough, I'm sure "none" is a slight exaggeration. Two effects I could see (but have no source for) are: 1. A slightly increased return radiation due to t

Fair enough, I'm sure "none" is a slight exaggeration. Two effects I could see (but have no source for) are: 1. A slightly increased return radiation due to the increased proximity of the heliopause and the the increased collision rate with the denser interstellar medium. The radiation from this should reach the surface of the Sun and slightly increase surface temps, but this effect would be dwarfed by the amount of radiation already coming from the Sun itself. 2. A tighter coupling of the Sun's magnetism to the stellar wind and interstellar magnetic field. This would slow down the Sun's rotation slightly, and it if increased differential rotation it could cause an increase in solar flare activity.