Lay the drapery on a flat surface, with the lined side facing up. Spread the fabric out so that you can easily access all the seams that are holding the lining in place.
Remove the seams using a clean, unused razor, seam ripper or an electric stitch remover. If you are using a razor, lightly run it over the stitches to cut through the thread without cutting the fabric of the drapery. Seam rippers and electric stitch removers are available at sewing and crafting stores.
Pull the threads out with your fingers or with a set of tweezers. Repeat until you have removed all the stitches along the seams. After removing the stitches along each side of the drapery, you should be able to gently pull the drapery fabric away from the lining. If the fabric does not easily pull free, check to see if you missed any stitches. Once all the seams are removed, discard the old liner.
Measure the draperies, starting at the bottom of the drapery rod pocket or pinch-pleated fold at the top to the hem at the bottom. Measure and cut the new thermal liner. It should be about 3 inches shorter and 4 inches narrower than the drapery fabric.
Fold the bottom edge of the thermal liner to form a 2-inch hem. Stitch the hem and lay the liner in place on the drapery.
Pin the liner into place by turning the bottom hem up, side edges in and the top hem over the liner, mitering the corners to create a smooth finish. The drapery fabric should conceal all raw edges of the liner. Sew all the seams to secure the liner into place and press the fabric to create sharp creases before hanging your drapery.