As shown by Christensen et al. [2] temperature-induced stresses or strains can have a strong influence on the frequency-dependent specific heat, especially of thin layers of viscoelastic materials near the glass transition. Thus, both the mathematical representation and the physical understanding of these couplings are essential for the interpretation of temperature-modulated DSC data. The approach provided in this paper is based on thermodynamics with internal state variables. It thus differs from the transfer-matrix method which has been applied in Refs. [2,29] and constitutes a thermodynamic basis from a different point of view for the interpretation of the results obtained in Refs. [2,29.32]. Furthermore, although not the object of this paper, time-domain simulations can also be done with the model presented thus allowing for the calculation of temperature-ramping experiments and effects observed therein [42]. The approach in this paper is restricted to one-dimensional states of stress and strain to focus on the main idea and keep the mathematical formalism to a minimum. The Gibbs free energy is chosen as thermodynamic potential and the primary variables -the stress and the temperature - are supplemented by a set of internal state variables which is introduced to include history-dependent and hence viscoelastic effects. The Gibbs free energy is approximated up to second order terms in the vicinity of a reference state. Employing the Legendre transform, a corresponding expression for the Helmhotz free energy is obtained. Evaluating the laws of thermodynamics, explicit frequency-dependent expressions for the specific heat under constant stress or strain, the thermal expansion behaviour as well as the mechanical response functions are obtained. Recently published formulations of the Prigogine-Defay ratio can also be derived from the proposed constitutive model. (C) 2009 Elsevier B.V. All rights reserved.