In order to understand the temperature-dependent response behaviour of thin thermoviscoelastic films which are deposited on relative stiff but thermally deformable substrates it is important to consider the lateral geometric constraints. They are generated by differences in the thermal expansion properties between the substrate and the film and provoke internal stresses. Since glass-forming materials exhibit distinct temperature history-dependent thermal expansion and calorimetric properties, primarily in the vicinity of the glass transition, the situation is rather complicated. In this article, a recently developed three-dimensional model of thermodynamics with internal variables is applied and adapted to simulate this type of behaviour. Explicit relations are obtained for the specific heat of the film, the normal strain and the lateral stresses. Numerical simulations demonstrate that the magnitude of the internal stress at temperatures below the glass transition depends strongly on the cooling rate. It is also shown that the specific heat of the supported film is principally different from the isobaric specific heat of the bulk material: the glassy limit of the specific heat of the film is reduced but the glass transition temperature is almost uninfluenced. The simulated behaviour is in accordance with experimental observations from literature. (C) 2012 Elsevier B.V. All rights reserved.