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The determinination of material properties is an essential step in the simulation of manufacturing processes. For hot deformation processes, consistently assessed Carreau fluid constitutive model derived in prior works by Schmicker et al. might be used, in which the flow stress is described as a function of the current temperature and the current strain rate. The following paper aims to extend the prior mentioned model by making a distinction, whether the material is being heated or cooled, enhancing the model capabilities to predict deformations within the cooling process. The experimental identifaction of the material parameters is demonstrated for a structural carbon steel with 0.54% carbon content. An approach to derive the flow properties during cooling from the same samples used at heating is presented, which massively reduces the experimental effort in future applications.