Minimally invasive heat therapies are of continued clinical interest to alter the functional attributes of tissue in the treatment of a number of pathologies. The extent of heating and tissue alteration is governed by the physics of the mode of heating, the geometry of the heater, and the properties of the tissue. Analytical models are needed to optimize the design of protocols and predict clinical outcomes. Presented here are the results of a finite difference model of the heating and alteration of a hypothetical non-perfused artery adjacent to a joule-heated, catheter-mounted balloon as might be used to enhance coronary angioplasty. The calculations suggest that shorter heating times (∼20 s) at greater balloon lumen temperatures (95 °C) better localize heating-induced changes to tissue than longer heating at lower temperatures (470 s at 60 °C) for the same alteration of the target arterial tissue.