Effect of MLT++ on the evolution of massive stars in the HR diagram. The various scatter points have the same meaning and color scale as in Figs. 1 and C.1. In the most massive stars, in which the density in regions with L_rad/L_Edd >  1 is so small that it limits the efficiency of convection, a temperature gradient becomes superadiabatic and a density inversion develops in order to stabilize the structure (see Appendix A). The MLT++ approach gradually smooths the temperature gradient and reduces superadiabaticy, also removing density inversions and the L_rad/L_Edd excess in the most massive stars. A direct consequence of the MLT++ treatment of convection is that the effective temperature becomes higher, as illustrated by the above figure.