Carbon fiber sheet material provides mechanical strength between the plates. The .004" thick carbon fiber is fixed to the plates with CA on both sides of the top and bottom plates. Eight strips approximately the length of the plate radius are needed. The fibers run across the gap between the plates. Alternatives: fiberglass would probably be an acceptable substitute to the carbon fiber and easier to use - this is used in the kit.
Balsa wood 1/4" x 1/8" serves three functions. It provides thermal insulation between the hot and cold plates. It adds an air tight seal. And it forms a mechanical beam in conjunction with the carbon fiber. The balsa is mounted with CA.