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−beta), and obtain the first sub-percent constraint on the temperature growth index 1−beta. Specifically, we find beta=(7.6+/-8.0)*1e-3 at the 68.3% confidence level.