Hello, I am not sure what the FES thinks about the dome model. Iv'e searched the wiki and FAQ, and I can't find any mention of it. Either way, I seem to have found an error. The sun, regardless of what model you accept, is the largest supplier of heat to the Earth and the hottest object in the system. The first law of thermodynamics states that energy cannot be created, so the sun must have a source of energy. Now this is not a problem for the round Earth model, which states that the sun's source of energy is fusion but I don't know how proponents of the dome model feel about that.
The first law of thermodynamics also states that energy cannot be destroyed. Where does the energy emitted by the sun go? Does it just stay here on Earth? If the system is isolated, then according to the second law of thermodynamics, the Earth and everything else in the system will increase in temperature until they are in thermodynamic equilibrium with the sun. The sun should be cooling and the Earth should be heating until they are the same temperature.