Are you talking about this?There is nothing closed about the solar system thermodynamically is there? If one looks at the massive amounts of energy contained in the quantum foam and that foam permeates the whole Universe (as far as we know) how can any system be considered closed or "somewhat closed"?
"Quantum foam, also referred to as spacetime foam, is a concept in quantum mechanics, devised by John Wheeler in 1955. The foam is a qualitative description of the turbulence that the phenomenon creates at extremely small distances of the order of the Planck length. At such small scales of time and space the uncertainty principle allows particles and energy to briefly come into existence, and then annihilate, without violating conservation laws."
Are you pretending this has anything to do with thermodynamic systems?
If you are talking about the background radiation, or the energy density of vacuum, the temperature change attributable to it is NEGLIGIBLE compared to the heat generated by the sun.
So yes, one can very well consider the solar system as a closed thermodynamic system.