A catheter apparatus carrying RF ablation electrodes on a helically configured portion of a flexible tube that can be inserted into the femoral artery of a patient, advanced into a renal artery, and then be manipulated to properly position electrodes carried by the helical tube to contact the endoluminal surface of the artery. While instrumentally monitoring the endoluminal surfaces temperature and impedance (measured with electrodes that are in an intimate contact with the surface), a low level of RF energy can be applied to selected sites on the interior (endoluminal) surface of the artery in order to ablate the renal sympathetic nerves without affecting the abdominal, pelvic, or lower-extremity nerves.