Top: time evolution of the temperature profile at the disk midplane for iterations i = [10, 15, 20, 25, 30]. The profiles indicate that thermal waves form and travel inward with time. There are two bump and shadow pairs at the end of the hydrostatic run for model MFID. The dotted blue line is the radiation temperature at i = 30 and the dashed black line indicates the background power law fit for the midplane T_law = 185 (R/au)^−0.5. Bottom: deviation of the temperature profile from the background power law.