Recent transition experiments by Jewell et al. in the high enthalpy T5 tunnel at GALCIT have shown turbulent spots on a 5 degree cone. In contrast to earlier experiments, such as for example at Purdue, the freestream was hot compared to the wall temperature. Because of the short duration of the experiments, the wall remained essentially at ambient temperature and thus was cold compared to the freestream. To date, no Direct Numerical Simulations are available for comparison with the experimental data. In this paper basic flow calculations for the T5 experiment Test Shot 2718 are provided, and also results from Direct Numerical Simulations are presented. Moreover, a Linearized Compressible Navier- Stokes code was developed that is employed for investigating the linear spatial stability. The stability investigations provide insight into the effects of the wall temperature on the linear stability behavior.