I, too, am concerned about the heat required to fuse the interfacing. Personally, I would purchase a lightweight neutral colored fabric, either a cotton or a poly lining and line each block before assembly. Just cut the lining (prewashed) the same size as the quilt square and zigzag them together with a very long stitch. Be sure the pretty side of the fabric is on top. Then you can treat it as one fabric and make your quilt the way you wish. You might need 3/8" seams to allow the zz to be inside the seam line.