Radiative-equilibrium dust temperature profiles of starless cores (upper) and protostellar envelopes (lower) for the isolated models (left) and their embedded variants (right). Subscripts of the curve labels (T₃₀ to T_0.03) indicate the model mass M (in M_⊙). The dashed horizontal lines in the upper panels continue the profiles of starless cores within the innermost radial zone. The dashed vertical line shows the outer boundary radius R = 10⁴ AU of all models. The maximum temperature and the inner boundary of the dusty protostellar envelopes are defined by the adopted dust sublimation temperature T_S = 10³ K. Three dashed horizontal lines in the lower panels indicate the range of radial distances over which the boundaries R₀ of the dust-free cavities are located for the model luminosities in the entire range of 0.03 − 30 L_⊙ (see Fig. 2). For protostellar envelopes with the same M, the “hotter” profiles correspond to higher L_⋆, larger R₀ (cf. Eq. (1)), and lower radial optical depths . Two dashed lines bracketing the profiles of protostellar envelopes indicate the slopes T_d(r) ∝ r^-0.88 and ∝ r^{− 1/3}, the latter describing the temperatures of a transparent dusty envelope with the adopted grain properties (see also Appendix A). Vertically aligned filled circles indicate the mass-averaged temperature T_M for each model, defined by Eq. (4). The slight wiggling of some profiles around their minima reflects the discrete nature of the Monte Carlo radiative transfer method.