Hi,
Nice sunroom!
One thought would be to distribute excess heat from the sunroom to the rest of the house. This keeps the sunroom itself from overheating, and provides some heat for the rest of the house.
If there is an accessible attic, maybe a vent in the sunroom ceiling ducted to a ceiling vent somewhere else in the house, with an inline Fantech type fan, and controlled by one of those replacement thermostats for attic vent fans (HD carries these).
Low mass sunrooms can be good home heaters:
PolySpace
Gary