A series of large eddy simulations are performed for a heated supersonic internally-mixed dual-stream jet issued from a converging-diverging circular nozzle. The study focuses on the modeling of the flow inside the nozzle and its effects on the external flow-field and radiated noise. The influence of mesh resolution, inlet conditions, inflow turbulence and wall modeling are investigated. The numerical predictions are compared to experimental PIV and far-field noise measurements from NASA Glenn Research Center. Overall the comparisons show good agreement, in particular for the refined simulation with dual stream inlet. Based on the results, isotropic mesh refinement and adaptation seems necessary in the noise-source containing region of the jet plume, as well as in the near-wall region inside the nozzle. Likewise, including the dual streams as inlet condition (rather than the core stream only) appears required, even for the present configuration with relatively low bypass ratio. The use of synthetic inflow turbulence and wall modeling inside the nozzle tend to yield thin perturbed boundary layers that transition to turbulent shear layer more rapidly and smoothly than the typical laminar boundary layer. This leads to a reduction of the peak velocity fluctuations in the shear layer near the nozzle exit and appears to prevent high-frequency noise associated with the laminar to turbulent transition.