The CMB temperature-redshift relation, TCMB(z)=T0(1+z), is a key prediction of the standard cosmology but is violated in many non-standard models. Constraining possible deviations from this law is an effective way to test the ΛCDM paradigm and to search for hints of new physics. We have determined TCMB(z), with a precision up to 3%, for a subsample (103 clusters) of the Planck SZ cluster catalog, at redshifts in the range 0.01–0.94, using measurements of the spectrum of the Sunyaev-Zel'dovich (SZ) effect obtained from Planck temperature maps at frequencies from 70 to 353 GHz. The method adopted to provide individual determinations of TCMB(z) at cluster redshift relies on the use of SZ intensity change, Δ ISZ(ν) at different frequencies and on a Monte Carlo Markov chain approach. By applying this method to the sample of 103 clusters, we limit possible deviations of the form TCMB(z)=T0(1+z)1‑β to be β= 0.012 ± 0.016, at 1σ uncertainty, consistent with the prediction of the standard model. Combining these measurements with previously published results, we get β=0.013±0.011.