Always test a small sample first to evaluate the results. Many novelty tweeds will have specialty yarns that may be heat sensitive. If in doubt, serge the ends of the fabric and have your dry cleaner preshrink the fabric.
To preshrink at home use this technique for both the fabric and the hair canvas interfacing: Fill a large bowl with water. Soak a large piece of muslin in the water and wring out excess. Lay the muslin over the fabric and press with the iron. The wet muslin will force steam into the fabric, preshrinking it. Carefully lift a section up and continue to treat the entire length of fabric, rewetting the muslin as needed. Once finished, the fabric will be damp. Lay the fabric out to dry completely before cutting. To preshrink the lining, steam well with a steam iron, using a press cloth.
Most tweed and bouclé fabrics can tolerate a wool setting on your iron, but it is important to test the fabric first, especially if there are a lot of novelty yarns, metallic fibers, or a high synthetic content. Take care not to flatten the fabric when pressing. Use a seam roll to press seams open. Steam the fabric lightly if the nap has been flattened. Use a press cloth when working on the right side of the fabric.
Once the fabric has been quilted, treat the pieces carefully and hang the garment to avoid having to press it again. The stitching lines for the quilting can be placed lining side up over a seam roll and pressed just along the stitching. If the entire garment is pressed once it has been quilted the impression of the outer fabric will show through on the lining and that imprint is difficult to remove.