A hybrid Lattice-Boltzmann Model (LBM) Very Large Eddy Simulation (VLES) solver for high-speed non-isothermal subsonic flows is used to simulate the unsteady jet flow exhausting from a single axi-symmetric nozzle, as well as the associated noise spectra and directivity. The jet exit Mach number and temperature ratio are set according to the various setpoints from the NASA SMC000 experimental campaign. Both isothermal and heated core flows are considered. The far-field noise is computed through a Ffowcs-Williams and Hawkings (FW-H) analogy applied to a fluid surface encompassing the jet plume. Both time- and frequency-domain formulations are used, the latter in combination with an azimuthal Fourier transform of the linear source terms to analyze the contribution of the different azimuthal components. A resolution study is carried out for both aerodynamic and acoustic results. The near- and far-field results confirm that the underlying flow features and noise mechanisms are fully represented by the numerical solution. A physical analysis of the source mechanisms for a heated core case is performed through a wavelet decomposition applied to the turbulent flow to separate the coherent flow motion, usually attributed to the hydrodynamic fluctuations, and the chaotic perturbations, which have a more dominant acoustic character. The two separated contributions extracted from the flow on the FW-H surface are used to compute the corresponding far-field acoustic contributions. Interestingly, noise is practically generated only by the coherent flow motion. Finally, the frequency-domain FW-H formulation is used to analyze the different azimuthal flow perturbation modes. Strong convection effect along the various modes are found.