Maximum temperature deviation in the disk’s midplane as function of the optical depth of the circumstellar disk. The solid line denotes the results for the frequency-dependent RT + gray FLD method. The dotted line denotes the results for the gray RT + gray FLD method. The dashed line denotes the results for the gray FLD method. The pluses “+” denote the deviations of the results of the various high-level radiation transport codes used in the original benchmark tests of Pascucci et al. (2004) and Pinte et al. (2009). These values are read off Figs. 4 and 5 in Pascucci et al. (2004) and Fig. 10 in Pinte et al. (2009).