Lightweight fusible interfacing will do what you need. The sales person at Joanne’s should be able to help you get the right one. The fusible is on one side, the other side is smooth & soft. Adds stability to lightweight fabrics and stretchy fabrics. I use it a lot on silks before cutting. They are Beautiful pieces. I hope you show us what you make.
You fuse the interfacing to the back of the fabric, and use a pressing cloth ( I use muslin) following the instructions with the interfacing I’ve never had any problems with melting any fabric. Fusible interfacing is used on silks and many delicate fabrics all the time.