A method for accelerating hemostasis of an artery having a puncture after arterial catheterization, the catheterization using a catheter introducer, the method including the steps of inserting into an artery a catheter introducer prior to arterial catheterization, following arterial catheterization, introducing a hemostasis device into the catheter introducer, such that a forward end of the hemostasis device lies exterior of the artery adjacent a puncture in a wall of the artery, accelerating hemostasis by heating blood in the vicinity of the puncture, thereby shortening the time required for hemostasis and following hemostasis, removing the catheter introducer and hemostasis device from the patient. A method for monitoring the progress of hemostasis of an artery is also disclosed.