The polymeric adhesive used for the bonding of thermoplastic and thermoset composites forms an insulating layer which causes a real problem for lightning strike protection. In order to make that interlayer electrically conductive, we studied a new group of electrically conductive adhesives based on hot melt copolyamides and multi-walled carbon nanotubes fabricated by the extrusion method. The purpose of this work was to test four types of hot melts to determine the effect of their viscosity on the dispersion of 7 wt % multi-walled carbon nanotubes and electrical conductivity. It was found that the dispersion of multi-walled carbon nanotubes, understood as the amount of the agglomerates in the copolyamide matrix, is not dependent on the level of the viscosity of the polymer. However, the electrical conductivity, analyzed by four-probe method and dielectric spectroscopy, increases when the number of carbon nanotube agglomerates decreases, with the highest value achieved being 0.67 S/m. The inclusion of 7 wt % multi-walled carbon nanotubes into each copolyamide improved their thermal stability and changed their melting points by only a few degrees. The addition of carbon nanotubes makes the adhesive’s surface more hydrophilic or hydrophobic depending on the type of copolyamide used.