A mathematical model is developed to evaluate the feasibility of an in vivo implanted drug delivery system. The delivery device consists of a cooling material coated by a drug-loaded thermoresponsive polymeric film. Drug release is initiated by remotely dropping the temperature of the cooling material sufficiently for the temperature throughout the polymer coating to drop below its volume phase transition temperature (VPTT), causing the polymer to swell and release the drug. Drug release switches off again when heat conduction from an external fluid medium raises the polymer temperature to above the VPTT causing the polymer to collapse. Candidate cooling mechanisms based on endothermic chemical reactions, the Peltier effect, and the magnetocaloric effect is considered. In the thin polymer film limit, the model provides an upper bound for the temperature the cooling material must be lowered for drug release to be initiated. Significantly, the model predicts that the duration a thin polymer will continue to release drug in a single cycle is proportional to the square of the thickness of the cooling material. It is found that the system may be realized for realistic parameter values and materials. A simple illustrative calculation incorporating the presence of a heat source is presented, and the results suggest that conduction due to the initial temperature difference between the water and the cooling material can make the dominant contribution to heat transfer in the polymer as it reheats to its VPTT.