Direct Numerical Simulations (DNS) were carried out to investigate the effect of wall heating and cooling on the primary and secondary instability regimes for a 7◦ half-angle straight (right) cone at Mach 6 and zero angle of attack. Typical flow conditions of the Boeing/AFOSR Mach 6 Quiet Tunnel (BAM6QT) at Purdue University was used for the numerical investigations. As expected, regarding the primary wall cooling resulted in a destabilization of the second mode and a stabilization of the first mode, while wall heating had the opposite effect. Wall cooling resulted in a slight reduction of the nonlinear primary wave saturation amplitudes. Wall heating changed the saturation behavior significantly. While for the reference (Tw = 300 K) and cooled wall cases the maximum second mode (saturation) amplitude remains nearly constant after saturation onset, the amplitude continued to increase in the heated case, although at a significantly reduced growth rate compared to the linear stage. In addition, grid convergence investigations showed that for a heated wall case a substantially finer grid resolution is required to accurately capture the primary wave (nonlinear) saturation process. The secondary instability investigations indicated that wall cooling results in larger secondary amplification rates.