Is the radiation temperature-redshift relation of the standard cosmology in accordance with the data?

The radiation temperature-redshift relation for Friedmann-Robertson-Walker geometries is rediscussed in connection with recent observational data base d on the fine-structure splitting of atomic and singly ionized carbon lines in quasar absorption-line systems. Indirect measurement of T(z) is one of the most powerful cosmological tests available because it may exclude even the presence of a cosmological constant. Unlike recent claims, we argue tha t the temperature at high z may be smaller than the standard prediction, th ereby opening a window to alternative (big bang) models. By including new i ngredients like a phenomenological decaying vacuum energy density and gravi tational 'adiabatic' photon creation as well as late inflationary models dr iven by a scalar field, a new temperature law is deduced and its prediction s are compared with the standard result.