An important target of many controlled release systems is to properly modify the drug release behaviour in response to some external stimuli like temperature or pH changes. The copolymer gels made up by poly(N,N-dimethylaminoethyl methacrylate (DMAEMA)-co-acrylamide (AAm)), being thermosensitive, are suitable systems for the thermocontrol of the solute release. Modifying the ratio DMAEMA/AAm, one may select the copolymer systems showing desired swelling properties. In order to better design such systems and in order to understand better the solute transport through the copolymer membrane, a mathematical model has been developed. The model employs suitable flux equations for the water uptake or release and for the solute (hydrocortisone) diffusion. With the condition of knowing the copolymer swelling kinetics, the model is able to describe in a reasonably good manner the solute transport across a DAEMA-AAm membrane undergoing step temperature changes.