(Left) Dust temperature-luminosity relation inferred from our single temperature model. The symbols are same as in Fig. 6. Red circles present the OFRG sample of Magnelli et al. (2010). The striped area presents results for SMGs extrapolated by Chapman et al. (2005) from radio and submm data. The Chapman et al. (2003) derivation of the median and interquartile range of the T_dust − L_IR relation observed at zs0 is shown by solid and dashed-dotted lines, linearly extrapolated to 10¹³   L_⊙. The dashed line represent the dust temperature-luminosity relation derived in Roseboom et al. (2011) for mm-selected sample observed with SPIRE and assuming a single modified blackbody model. (Right) Dust temperature-luminosity relation inferred from our power-law temperature distribution model. Symbols are the same as in the left panel. The red dashed line presents the T_c − L_IR relation inferred from a least-square second degree polynomial fit.