"Sunroom" Venting

I have a question regarding venting in an addition to my home.

The room is built on top of the garage of the house but is attached only to the outside wall of the house, not really part of the main house. It is currently shut off from the house only by a window which is the only way to enter the room which was apparently used as a greenhouse by previous owners. the couple we bought the home from added an asphalt shingle roof to the room. the walls of the room are insulated but not the ceiling. Right now the ceiling is open rafters with no insulation. There is no overhang of the roof, no soffit and no venting.

I have been picking away at working on the room to turn into a sitting room. It won't be heated from inside the room unless we are in the room, so the majority of the time it will be empty and unheated. It will also be shaded in the hotter months by nearby trees. I am looking at adding 2in rigid insulation to the ceiling for insulation, the ceiling afters are 2x6 so there will be some gap between the insulation and roof. Do I need to add ventilation in the ceiling? And what would be the best way to do it if I need to?

Thanks!!

 

Always best to add your location to your profile, sure help with questions like this or code questions.
Not cheap to do and not a good DIY job but the best way would be to have the ceiling spray foamed in your case.
2" of foam would not be nearly enough insulation in about 99% of the US.
https://www.energystar.gov/index.cfm...sulation_table
It also will need to be covered with sheet rock.