Temperature profiles (upper panel) in the midplane of the circumstellar disk for the case of low optical depth τ_550 nm = 0.1. In the lower panel the deviations of the three different radiation transport methods to the comparison code result are displayed. Solid lines denote results for the frequency-dependent RT + gray FLD method. Dotted lines denote results for the gray RT + gray FLD method. Dashed lines denote results for the gray FLD method. Pluses “+” denote results for the comparison code RADMC. In this optical thin case, the results for gray RT + gray FLD are almost identical to the frequency-dependent RT + gray FLD. Here, analytical estimates for the optically thin approximation are given: crosses “×” mark the analytical estimate by Spitzer (1978) for irradiated regions far away from the star, circles “o” mark the analytical estimate in the gray and isotropic approximation (T ∝ r^−1/2).