In this paper, the flow and acoustic characteristics of an aerospike nozzle jet at a Nozzle Pressure Ratio (NPR) = 3 and three different Temperature Ratios (TR) = 1, 3, 7 are presented. Implicit Large Eddy Simulations (ILES) are deployed to simulate the flow of the aerospike nozzle. The LES calculations are completed by aeroacoustic computations based on the Ffowcs Williams-Hawkings (FWH) equation. In the supersonic jet exhausting an aerospike nozzle, two shock-cell structures are observed: an annular and a circular one. In the direct vicinity of the annular nozzle, the annular jet is non-attached and reattaches further downstream at increasing distance with increasing jet Temperature Ratio (TR). The observed shock cells in the non-attached annular jet structure are longer for TR3 and TR7 compared to TR1. The shock strength in the annular jet is increasing with increasing jet TR. In the meantime, the total number of shock cells in the circular part of the jet decreases with increasing jet TR. Pressure spectra in the near-field show the presence of a strong tonal noise at upstream angles corresponding to screech tones. Two-point cross-correlations of pressure data acquired in monitoring points located along axial lines in the circular shear layer are computed to quantify the upstream propagating waves associated to this tonal component. Power spectral density of the radial velocity at several monitoring points located at the shock cells as well as at the separation bubble, highlights the main oscillation modes of the annular shock-cell structure. Supersonic convection velocities of turbulent structures are detected with increasing jet temperature by means of two-point cross-correlation. This confirms the presence of Mach waves observed in the instantaneous snapshots. The Mach waves radiation angles are in agreement with existing models. In the far-field spectra, the highest Sound Pressure Levels (SPL) are associated to those Mach waves at angles around 140° (TR3) and 120° (TR7). High skewness and kurtosis in the pressure signals indicate crackle noise at higher jet temperatures. Additionally, the shock-cell length is used to predict the central frequency of Broadband Shock-Associated Noise (BBSAN) as a function of observation angles. The far-field spectra display mixing noise as well as BBSAN, related to the interaction between the convected vortices in the shear layers and the shock-cell structure. With increasing jet temperature, higher SPL are detected in agreement with the BBSAN central frequencies which were computed using the annular and circular shock-cell length.