Prefabricated, lightweight building elements are widely used in the building construction sector. Such elements consist of fibrous thermal insulation encapsulated between two metal sheets. Under various circumstances, moisture can appear in the insulation matrix. Since the temperature of the boundary metal sheets changes dynamically with meteorological conditions, heat and mass transfer between boundaries appear in this case. This paper presents a transient model of the heat and mass transfer, including the sorption and condensation processes. A numerical model considers the dynamical changing of the boundary temperatures. A parametric study considering different amplitudes of temperature change, different moisture masses and different thicknesses of the insulation matrix was made. It was found that a relatively small mass of water in the insulation matrix can result in a significantly increased average heat flux during a periodic cycle. The numerical code was verified with experiments, which showed good agreement with the numerics. (C) 2011 Elsevier Ltd. All rights reserved.