Although utilizing phase change materials (PCMs) for thermal energy storage and management has remarkably grown, the reliance on petroleum-based PCMs has raised concerns about their sustainability. Hence, in this study, the mixture of beeswax (BW) and coconut oil (CO) as a new biological-based PCM (bio-PCM) was developed. Also, the effect of 0.5, 1, and 2 wt% of graphene-copper (Gr-Cu) hybrid nanoparticles on the bio-PCM's ability in thermal energy storage (TES) was scrutinized. Thermal, chemical, physical, and stability specifications of BW-CO/Gr-Cu nano- and bio-based PCMs (bio-nPCMs) were examined by Differential Scanning Calorimeter (DSC), Fourier Transform Infrared Spectroscopy (FTIR), X-ray diffraction (XRD), and thermogravimetric analysis (TGA). Also, the thermal conductivity of bio-PCM and bio-nPCMs were explored in a range of temperatures from 25 to 60 °C. FTIR indicated no chemical reactions or new synthesis materials in the final composite. Also, all the used materials were recognized by XRD. DSC analysis showed that melting and solidification of bio-PCM start at 51 and 56 °C while adding 2 wt% Gr-Cu nanoparticles reduced the temperatures to 49.9 °C and 53.8 °C, respectively. In addition, bio-PCM had latent heats of 172.3 kJ/kg and 173.11 kJ/kg for melting and solidification, whereas 2 wt% Gr-Cu nanoparticles shifted them to 160.75 kJ/kg and 167.45 kJ/kg, in respect. On the other hand, the higher the concentration of Gr-Cu in the base PCM, the higher the thermal conductivity of bio-nPCMs maximally about 604 % higher than that of the base bio-PCM at T = 25 °C. Furthermore, a new model was proposed for the thermal conductivity that had an average error of 5 %. Machine learning was employed to estimate the thermal conductivity and latent heat. The former with R-squared, mean error (MSE), and average absolute relative deviation (%AARD) of 0.9996, 1.1253 × 10−4, 1.871, and the latter with 1, 4.7 × 10−10, and 0.01, respectively. The outcomes of this study present a procedure to develop future bio-PCMs and hybrid nanoparticles to pave the way to reaching net-zero carbon.