Restriction of blood flow by the narrowing or occlusion of arteries is one of the most common presentations of cardiovascular disease. One treatment involves the introduction of a metal scaffold, or stent, designed to prevent recoil and to provide structural stability to the vessel. On the occasions that this treatment is ineffective, failure is usually associated with re-invasion of tissue. This can be prevented by local delivery of drugs which inhibit tissue growth. The drug might be delivered locally in a polymer coating on the stent. This paper develops and explores the use of a thermal analogue of the drug delivery process and the associated three-dimensional convection-diffusion equation to model the spatial and temporal distribution of drug concentration within the vessel wall. This allows the routine use of commercial finite element analysis software to investigate the dynamics of drug distribution, assist in the understanding of the treatment process and develop improved delivery systems. Two applications illustrate how the model might be used to investigate the effects of controllable or measurable parameters on the progression of the process. It is demonstrated that the geometric characteristics of the stent can have significant impact on the homogeneity of the dosing in the vessel wall.