Observed temperature function of local clusters (red dots), with error bars defined as the sum of the inverse-square detection volumes of the clusters. The best-fit theoretical models are also shown, in the case of the mass function of SMT (blue dashed curve), and the mass function of Tinker et al. (2008), with and without a fixed index β_TM (defined in Eq. (28)) for the M − T scaling law (solid green and dot-dashed purple curves, respectively).