If you haven't worked with carbon fiber before, you may be surprised to learn that is a surprisingly good conductor of electricity. Not as good as aluminum, but far better than most materials.
For example: I have a piece of 16mm OD, 13mm ID thin wall carbon fiber tubing. A piece 16" long has a measured resistance of less than 10 ohms. I put 5 Amps through the tube, and it got hot quickly, so you could use a carbon fiber tube or sheet as a heater - if you keep in mind that the stuff can't tolerate high temperatures unless you buy special high-temperature material. Using high-temp material, you could build a heated bed for a 3D printer.
In building multirotor aircraft, I like my designs to have a clean look, which usually means running the motor wires through the arms. The ends of carbon fiber tubes are sharp - sharp enough to cut through the silicone insulated wires that I use. So I had to print some special plastic grommets to slide into the ends of the tubes. The grommets are rounded, so it won't cut the insulation, and even if it did, the plastic grommets are non-conductive.