The present work is aimed to examine how the HTC and main 3D passage aerodynamic features may be affected by a non-adiabatic wall temperature condition. A systematic computational study has been firstly carried out for a 3D NGV passage. The impacts of wall temperature on the secondary flows, trailing edge shock waves and the passage flow capacity are discussed, underlining the connection and interactions between the wall temperature and the external aerodynamics of the 3D passage. The local errors in HTC in these 3D flow regions can be as high as 30-40\% if the wall temperature dependence is not corrected. The effort is then directed to a new 3-point non-linear correction method. The benefit of the 3-point method in reducing errors in HTC is clearly demonstrated. A further study illustrates that the new method also offers much enhanced robustness in the wall heat flux scaling, particularly relevant when the wall thermal condition is also shown to influence the laminar-turbulent transition exhibited by two well-established transition models adopted in the present work.