Newark Dressmaker supply has a package of fusible interfacing that is 15" x 3 yards long. The price is $1.35. They also offer Heavy Duty Wonder Under, that is 17" wide and comes in packs of 1 yard for $2.35.http://www.newarkdress.com/page155.html#845
If you were unable to find any of the fuseable materials locally, these are great mail order sources.
Even after you fuse the design to the other T-Shirt, you will still probably want some kind of finish around the edge of the design piece. If you know someone who sews I would recommend turning under the edge of the design and stitching it to finish the raw edge. Once you have it fused in place it would be best to top stitch around the edge so it adheres firmly to the T-Shirt underneath.
Good luck with your project!