Sustainable composite materials, including carnauba wax, can store energy in the form of latent heat, and containing the wax may allow form-stable melting and crystallization cycles to be performed. Here, it is shown that carnauba wax in the molten state and the abundant nanoclay montmorillonite form stable composites with mass ratios of 50–70% (w/w). Transmission electron microscopy analysis reveals the inhomogeneous distribution of the nanoclay in the wax matrix. Analyses with infrared and multinuclear solid-state nuclear magnetic resonance (NMR) spectroscopy prove the chemical inertness of the composite materials during preparation. No new phases are formed according to studies with powder X-ray diffraction. The addition of the nanoclay increases the thermal conductivity and prevents the leakage of the phase change material, as well as reducing the time intervals of the cycle of accumulation and the return of heat. The latent heat increases in the row 69.5 ± 3.7 J/g, 95.0 ± 2.5 J/g, and 107.9 ± 1.7 J/g for the composite materials containing resp. 50%, 60% and 70% carnauba wax. Analysis of temperature-dependent 13C cross-polarization solid-state NMR spectra reveal the enhanced amorphization and altered molecular dynamics of the carnauba wax constituents in the composite materials. The amorphization also defines changes in the thermal transport mechanism in the composites compared to pure wax at elevated temperatures.