Sunrooms allow the radiant heat of the sun to beat into the room. This heats moisture in the air and increases the amount of relative humidity. When the moist air is heated it will expand and look for a cold spot to condense, on your windows.
Where does the relative humidity come from you may ask? Well, moisture can enter the room every time you open the door out into the sunroom and also comes from air leakage from the heated living space of your home.