More and more, old food packages should be recycled as new food packages, in spite of the fact that they could be contaminated. In order to protect food from pollution, the new packages consist of bi- or tri-layer polymers, the recycled polymer being surrounded with virgin polymer layers playing the role of functional barriers. As these polymer layers are prepared by co-extrusion at the melting temperature, a diffusion of the contaminant takes place during this short stage. A numerical model with finite differences is built, taking into account the heat transfer by conduction through the polymers and by convection at the external surface, and the diffusion of the contaminant through the polymer layers with a temperature-dependent diffusivity. The results are expressed in terms of profiles of concentration developed through the thickness of the packaging. Dimensionless numbers are used so as to draw master curves of use in various typical cases.