  In the standard hot cosmological model, the black-body temperature of the
Cosmic Microwave Background (CMB), $T_{\rm CMB}$, increases linearly with
redshift. Across the line of sight CMB photons interact with the hot
($\sim10^{7-8}$ K) and diffuse gas of electrons from galaxy clusters. This
interaction leads to the well known thermal Sunyaev-Zel'dovich effect (tSZ),
which produces a distortion of the black-body emission law, depending on
$T_{\rm CMB}$. Using tSZ data from the ${\it Planck}$ satellite it is possible
to constrain $T_{\rm CMB}$ below z=1. Focusing on the redshift dependance of
$T_{\rm CMB}$ we obtain $T_{\rm CMB}(z)=(2.726\pm0.001)\times (1+z)^{1-\beta}$
K with $\beta=0.009\pm0.017$, improving previous constraints. Combined with
measurements of molecular species absorptions, we derive $\beta=0.006\pm0.013$.
These constraints are consistent with the standard (i.e. adiabatic, $\beta=0$)
Big-Bang model.

Cosmology and Nongalactic Astrophysics