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) = T0(1 + z), where T0 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) = T0(1 + z)^(1−β) , and obtain the first sub-percent constraint on the temperature growth index 1 − β. Specifically, we find β = (7.6 ± 8.0) × 10^(−3) at the 68.3% confidence level
