We report the welding of thermoplastic materials by means of embedded fully-aligned carbon nanotube (CNT) web. Layers of CNT web (each layer of which has a densified thickness of 50 nm) were placed between two polyether ether ketone (PEEK) films to create a resilient insert which was then embedded between two bonding interfaces. An electrical current was passed through the CNT webs to activate Joule heating, melting the insert and adjacent surfaces of the thermoplastic parts. Preliminary experiments on welded PEEK samples show that the tensile strength of the welded specimens reached 96% of the strength of the pristine material, even before optimizing the processing conditions. The potential of this welding technology is evident: the inserts are ultra-thin, highly flexible, so can conform to bonding surfaces of complex shape, and the anisotropy of the CNT-web provides an additional variable for optimizing the electro-thermal response.