Analytical solutions were developed for the time lag and steady-state transdemal flux of drugs across a heat-aided drug-delivery device. The expressions include thermodynamic and physical properties of the solvent/medicament and membrane system, making the approach amenable to in silico evaluation of process performance in a spreadsheet-like environment. Methods and concepts from classical control theory were applied to predict the onset of the steady-state flux. The strategy employed was based on the system's time constant, computed by taking the inverse of the first eigenvalue of a Sturm-Liouville problem. This framework does not require a solution to the transient heat-enhanced diffusion problem and relaxes the assumption of a constant diffusion coefficient throughout the membrane. The results match published data, partially explain some clinical trial observations, and suggest a novel method to control the plasma drug concentration.