I have discussed many times the insulation properties of window coverings in previous posts. Such products as cellular shades offer very high R Values. In my session, An Architect’s Guide to Sustainable Window Coverings, I also address the role of drapery and roman shades.
As you can see in the graphic below, drapery does an excellent job in trapping air, which serves as an insulator. What I would like to point out is that a double lined drapery performs over 300% better then an unlined drapery.
The Roman Shade, the way we construct it at Decorating with Fabric also provides excellent insulation properties. Take a look at the graphic below. Notice how the air pockets are created in the space between the face fabric and the lining.