I would NOT use any invisible thread especially on a heavy weighted t-shirt quilt. Look once again at the designs on each shirt and see if there is some way you can quilt around the design. It will take more time in changing thread to match whatever it is you are quilting but the quilt will last a lot longer. If you can, post pictures of the t-shirts and maybe we can give you some suggestions on designs to use to quilt each block. Good Luck !!