Details of the temperature model adopted for the cores. Top panel: Calibration of the clump L/M with the rotational temperature of CH₃C₂H, edited from Molinari et al. (2016a). The vertical dashed red lines mark different ranges of L/M as done in our work. The horizontal dashed green line mark the 35 K temperature value fitting the point within the 1 − 10 L_⊙/M_⊙ range, which has been adopted in this work for the correspondent evolutionary group. The full black line represents the power law fitting the points at L/M > 10L_⊙/M_⊙ (see Molinari et al. 2016a), also adopted in this work. Bottom panel: Overall distribution of the assumed core temperatures as a function of the clump L/M, resulting from the model used in this work. The vertical dashed red lines serve as in the top panel.