Free-stream turbulence preceding high-pressure turbine blades has a crucial impact on blade fields including the heat transfer on the wall. Many parameters characterize this turbulence; its intensity, length scales and physical spectrum are addressed in the study of various operating points of the LS89 configuration. Usually, operating points where weak turbulence is injected are well predicted for all fields by Direct Numerical Simulations (DNS) and Large Eddy Simulations (LES). The MUR235 operating point however, with an experimentally injected turbulence level of 6%, remains incorrectly predicted when imposing the experimental values in the simulations. Such difficulties raise many questions amongst which mesh size and turbulent kinetic energy spectrum are of specific importance for LES. Going away from synthetic turbulence injection by imposing a physical energy spectrum can help improving the prediction of heat transfer. From the present study, it seems that turbulent spots developing in a pre-transition region for higher levels of turbulence on the suction side are important features to capture for proper predictions. In parallel, typical structures of boundary layers such as streamwise oriented vortices have been observed and their existence conditions the heat transfer field on the blade wall. From this specific study, all of these physical processes are seen to be highly dependent on the turbulent specification and turbulent transition observed for the MUR235 case. Depending on these inflow specifications, a transitional boundary layer may be encountered upstream of the shock thus modifying the heat transfer profile.