  The relation between redshift and the CMB temperature, $T_{CMB}(z)=T_0(1+z)$
is a key prediction of standard cosmology, but is violated in many non-standard
models. Constraining possible deviations to this law is an effective way to
test the $\Lambda$CDM paradigm and search for hints of new physics. We present
state-of-the-art constraints, using both direct and indirect measurements. In
particular, we point out that in models where photons can be created or
destroyed, not only does the temperature-redshift relation change, but so does
the distance duality relation, and these departures from the standard behaviour
are related, providing us with an opportunity to improve constraints. We show
that current datasets limit possible deviations of the form
$T_{CMB}(z)=T_0(1+z)^{1-\beta}$ to be $\beta=0.004\pm0.016$ up to a redshift
$z\sim 3$. We also discuss how, with the next generation of space and
ground-based experiments, these constraints can be improved by more than one
order of magnitude.
