Device and method for heating tissue, the device having a catheter shaft for insertion into a patient's body, a chamber formed by a collapsible balloon mounted on the catheter shaft and filled with an electrically conductive fluid, two or more electrical contacts enclosed within the chamber, a power supply for applying an electrical potential to the contacts, and a two or more conductors for connecting each of the contacts to the power supply. The fluid is heated on the basis of I.sup.2 R losses by a radio frequency electric current flowing between the electrodes, and the fluid in turn heats the surrounding tissue by heat transfer through the wall of the chamber. According to the method, the apparatus is inserted into the patient's body, the chamber is filled with an electrically conductive fluid, and an electrical potential is applied to the contacts. The apparatus functions as a temperature source. A thermister sensor in the balloon or in contact with tissue responds to the heating effect to control the application of the current. Advantageously, by periodic sensing of temperature, and application of controlled rf power, a preset constant temperature is maintained at the selected sensing point, either at the internal body site or the liquid within the balloon. In this way carefully controlled therapy can be conducted at constant temperature.