Calculation of accurate wall heat flux for high enthalpy flows requires a dense grid system, which leads to significantly large computational time. A high-order scheme can improve the efficiency of calculation because wall heat flux can be obtained accurately even with a relatively coarse grid system. However, conventional high order schemes have some drawbacks such as oscillations near a discontinuity and instability in multi-dimensional problem. To resolve these problems, enhanced Multi-dimensional Limiting Process(e-MLP) was applied as a high-order scheme. It could provide robust and accurate solutions with high order accuracy in calculation of high enthalpy flows within a short time. We could confirm the efficiency of the high order e-MLP scheme through grid convergence tests with different grid densities in a hypersonic blunt nose problem.