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 subpercent constraint on the temperature growth index 1 -β . Specifically, we find β =(7.6 ±8.0 )×10-3 at the 68.3% confidence level.