A catheter device and method for heating tissue, the device having a catheter shaft constructed for insertion into a patient's body, and at least one chamber mounted on the catheter shaft. The catheter shaft has at least one lumen for fluid flow through the shaft. The chambers are defined by walls that are at least in part expandable. Fluid flows, through the lumens, between the chambers and a fluid source outside the body. The chambers can be filled with the fluid after they have been placed within the body. A heating device heats liquid within at least one of the chambers, so that heat is transmitted from the liquid to surrounding tissue by thermal conduction through the wall of the chamber. Means are provided for selectively directing heat transmission toward a selected portion of surrounding tissue. The chambers are fillable with fluid separately from each other, so that the chambers can occupy any of a plurality of possible total volumes. By selecting the total volume of chambers, compression of the tissue can be controlled, and hence the effectiveness of transfer of heat to the tissue can be controlled. According to the method, the catheter device is used to heat tissue from within a duct in a patient's body. The chambers are inserted into the duct and filled with fluid. Liquid is heated within at least one of the chambers, and heat is selectively directed toward a selected portion of surrounding tissue.