Main panel: dust temperature as a function of the IR (8−1000 μm) luminosity for the PHz-IRAM sources (full stars, red for secure CO line identifications, and blue for the uncertain ones). The shaded orange area shows the local T_dust − L_IR relation derived by Chapman et al. (2003), linearly extrapolated to 10¹³ L_⊙. The shaded cyan area shows the range of dust temperatures for main sequence galaxies in the redshift range of the PHz-IRAM sources (1.3 < z < 2.8) according to the relation found by Magnelli et al. (2014), and extended to L_IR > 10¹³ L_⊙. The shaded green area presents results for z ≃ 2 SMGs from Chapman et al. (2005). The purple diamonds represent the relation found for z < 1.5 SPIRE sources by Symeonidis et al. (2013). Top and right panels: distributions of SFR (and IR luminosity) and dust temperature, respectively, for all PHz-IRAM sources.