The glass transition is a central physical phenomenon in polymeric materials. It is related with significant changes of the thermomechanical properties and pronounced process-dependent behavior. This work deals with process-dependent caloric behavior in the glass transition regime which is known as enthalpy relaxation. Based on Coleman-Noll procedure and the scheme of linear irreversible thermodynamics, a model of enthalpy relaxation is derived and analyzed. Therefore, an internal temperature is introduced as internal variable and the analogy with viscoelasticity is utilized. The non-equilibrium part of the entropy is identified as thermodynamic driving force. For a purely temperature-dependent relaxation time of the internal temperature, the qualitative behavior of the model is discussed. Furthermore, the model parameters are examplarily adapted for polystyrene. In a first step, rate-independent behavior of the heat capacity in glassy and equilibrium is approximated by linear functions. Subsequently, the parameters for the evolution equation of the internal temperature are identified based on the reduced heat capacity. By comparing two different temperature rates, a rate-dependency of the relaxation time is observed. Therefore, the model is extended by a rate-dependency function for the relaxation time where temperature- and rate-dependency are multiplicatively splitted.