Temperature profile of the outermost layers of a 110 M_⊙ star computed with the MLT++ method of MESA. The method artificially reduces the difference between ∇_T and ∇_ad in the stellar envelope, acting as an source of additional envelope mixing (see Sect. 4.3 for details). The small envelope mixing used here is not enough to suppress density inversions completely (panel c) but it does help to keep the specific entropy small (panel d), gas pressure fraction non-negligible (panel e) and therefore time steps reasonable.