Abstract: The e^N method predicts transition based on the level of the linear amplitude amplification of the disturbances in the boundary layer. Boundary layers over cones at Mach 6 were investigated with different nose bluntness and under different wall temperature conditions. Combined with direct numerical simulation (DNS) and parabolized stability equations (PSE), from the viewpoint whether the e^N method is able to accurately describe the amplification of the disturbances in the above boundary layers, its reliability for transition prediction was interrogated. Results show that in the cases of small bluntness or high wall temperature, the disturbances undergo the intermodal exchange from the first mode to the second mode when travelling downstream in the boundary layer, so that the e^N method based on linear stability theory becomes less reliable. Under the same wall temperature condition, as the nose bluntness increases, the e^N method is more reliable. For the same nose bluntness, as the wall temperature decreases, the e^N method is more reliable. Since linear stability theory always underestimates the amplification of the disturbances when there is an intermodal exchange, for the given transition criterion N_T, which could be calibrated by a certain case, as the bluntness decreases or the wall temperature increases to some extent, the e^N method tends to produce a further downstream transition location than reality. To recalibrate the transition criterion, the smaller the nose bluntness or the higher the wall temperature, the larger the modification of N_T factor.