An enhanced method and device are provided to treat atrial fibrillation or inhibit or reduce restenosis following angioplasty or stent placement. A balloon-tipped catheter is disposed in the area treated or opened through balloon angioplasty immediately following angioplasty. The balloon, which can have a dual balloon structure, may be delivered through a guiding catheter and over a guidewire already in place. A fluid such as a perfluorocarbon flows into the balloon to freeze the tissue adjacent the balloon, this cooling being associated with reduction of restenosis. A similar catheter may be used to reduce atrial fibrillation by inserting and inflating the balloon such that an exterior surface of the balloon contacts at least a partial circumference of the portion of the pulmonary vein adjacent the left atrium. In another embodiment, blood perfusion is performed simultaneously. In another embodiment, tissue contacted by the cryoablation catheter, undesired to be ablated, is protected against damage by a separate heating step.