How can I insulate my sunroom ?

Only use the foam board at night. Cover it with something pretty so if you lean it against the walls during the day, you won't mind looking at it. The sun will keep the sunroom warm during the day. Also - use insulated drapes in addition to the foam board at night.

in grocers cold rooms, clear heavy plastic or vynail to keeps the cold in. think clear curtains. do you have cement floor? it can act as a heat sink if the angle of the sun can get to it. caulking can be your friend....take a lit incense stick- the smoky ones, see where air is getting in or out. caulk the spot. an electric fire place could help warm up the area.

Are you wanting to insulate the sun room or are you wanting a prettier option for the connecting opening?

Maybe you can make framed "glassed" doors with green house polycarbonate panels. They wouldn't insulate as well as your foam boards but they have a pleasing reeded glass look for day use.

If you're getting drafts from the sun room windows you can use the ole "plastic sheeting and hair dryer shrink wrap" hack.

A step up would be installing storm window panels...don't they add a smidge of "double paned" insulating value?

Depending on age of the house, you may be correct that there is no insulation in the walls. My 1950’s fixer doesn’t have any insulation in the walls. Cellulose fiber can be blown in, but it settles ove time. ...leaving the place cold. William, who lurks on this web site was a huge help in getting my place weather sealed. If you do keep the foam board, put it behind dry wall. It can off gas if a fire happens.

Have you tried adhering bubblewrap to the glass, trather than the plastic sheets? Alternatively, you could try attaching a 2nd layer of heavier plastic sheeting. A 9 x 7.5 ' opening admits a terrific amount of cold air. Can you make the opening smaller?

Check out William's other posts on this site re: insulation options.

Using mirrors will bounce more light into adjacent rooms.