© 2015 American Physical Society. The relationship between the cosmic microwave background radiation temperature and the redshift, i.e., the T-z relation, is examined in a phenomenological dissipative model. The model contains two constant terms, as if a nonzero cosmological constant Λ and a dissipative process are operative in a homogeneous, isotropic, and spatially flat universe. The T-z relation is derived from a general radiative temperature law, as appropriate for describing nonequilibrium states in a creation of cold dark matter model. Using this relation, the radiation temperature in the late Universe is calculated as a function of a dissipation rate ranging from μ=0, corresponding to a nondissipative lambda cold dark matter model, to μ=1, corresponding to a fully dissipative creation of cold dark matter model. The T-z relation for μ=0 is linear for standard cosmology and is consistent with observations. However, with increasing dissipation rate μ, the radiation temperature gradually deviates from a linear law because the effective equation-of-state parameter varies with time. When the background evolution of the Universe agrees with a fine-tuned pure lambda cold dark matter model, the T-z relation for low μ matches observations, whereas the T-z relation for high μ does not. Previous work also found that a weakly dissipative model accords with measurements of a growth rate for clustering related to structure formations. These results imply that low dissipation is likely for the Universe. The weakly dissipative model should be further constrained by recent observations.