New high-performance epoxy-based nanocomposite adhesive materials were developed with the innovative use of nanomaterials to enhance the bond strength, especially at elevated temperatures. A tetraglycidyl diaminodiphenylmethane (TGDDM) based aerospace-grade epoxy adhesive (EA9396) with a high glass transition temperature and viscosity was combined with functionalized CNFs and a phase-separated poly(styrene)-poly(butadiene)-poly(methyl methacrylate) triblock copolymer (SBM). The ozone-treated CNFs (OZ-CNFs) were functionalized with polyethyleneimine dendrimer (PEI + OZ-CNFs), or a polyamine hardener (H + OZ-CNFs) and characterized using X-ray photoelectron spectroscopy (XPS), infrared spectroscopy (FTIR) and thermogravimetric analysis (TGA) to confirm the chemical reaction of the amine functional groups. Room temperature mechanical testing revealed the optimized nanocomposite adhesives containing SBM and CNFs functionalized with either PEI or hardener resulted in a 40% increase in lap shear strength (50 MPa) when compared to the unmodified epoxy (35.6 MPa). At the elevated temperature of 90 °C, a strength improvement of 35% and 38% (29.5 MPa and 30 MPa) was observed for the adhesives containing SBM and CNFs functionalized using PEI or hardener, respectively. SEM images showed that CNF functionalization provided a more uniform distribution in the adhesive and enhanced the SBM plastic deformation during crack propagation. The PEI and hardener functionalization also significantly reduced the level of CNF pull-out, which was believed to enhance the energy dissipation mechanisms responsible for the significant increase in the lap shear strength.