  The redshift dependence of the cosmic microwave background temperature is one
of the key cosmological observables. In the standard cosmological model one has
$T(z)=T_0(1+z)$, where $T_0$ is the present-day temperature. Deviations from
this behavior would imply the presence of new physics. Here we discuss how the
combination of all currently available direct and indirect measurements of
$T(z)$ constrains the common phenomenological parametrization
$T(z)=T_0(1+z)^{1-\beta}$, and obtain the first sub-percent constraint on the
$\beta$ parameter, specifically $\beta=(7.6\pm8.0)\times10^{-3}$ at the
$68.3\%$ confidence level.
