A catheter-based device tracks over a guidewire which has been placed from a first blood vessel into a second blood vessel. The distal tip of the catheter is advanced into the second vessel while a proximal member remains in the first vessel. Matching blunt tapered surfaces on each of the distal tip and the proximal member are clamped together, with adjacent walls of each vessel between them, after which a known, controlled pressure is applied between the two surfaces. Heat energy is then applied to the blunt surfaces for approximately 1-30 seconds to weld the walls of the two vessels together. After coaptation of the vessel walls, the heat is increased to then cut through the vessel walls to create a fistula of the desired size.
