It can be modeled as inviscid but I would not expect the simulation results to be accurate. The viscous effects will not be captured and hence, there will be an increase in temperature and Mach number as you are seeing.
Make sure you have a good mesh, well refined at the boundaries.
Check the solution methods with the best practice, we have a tutorial on hypersonic.
Use the high speed numerics which will help in convergence.
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