Vertical temperature distributions of a protoplanetary disk calculated with our method and with the “diskstruct” package written by C. Dullemond. More specifically, the results from the “distruct-fullrt” method with the full treatment of the frequency and angular dependent radiative transfer are shown with the thick blue lines. The thick red curves represent the results from the approximate “diskstruct-vertrt” method, which adopts gray opacities for the dust thermal radiation. The temperature distributions calculated with our method are shown with the thin black lines. The presented vertical distributions are calculated for three radial positions in the disk, namely for R = 1 AU (top), R = 10 AU (middle), and R = 100 AU (bottom) for an optically thick protoplanetary disk illuminated by a star with T_eff = 6000 K.