Variation of the temperature slope with time, as determined at the disk midplane of a massive star with the simulations by Kuiper & Hosokawa (2018, their Fig. 6), with the corresponding stellar mass indicated on top. The k_sim is the meanlinear variation determined over the range of radii, 100–2000 au. The red dashed line marks the observed value fitted in the upper panel of Fig. 3, and the grey shadow defines the dispersion about the best fit (1σ).