An electrode structure for use in emitting electromagnetic radiation for localized heating of tissue in medical therapy and capable of permitting deep heat penetration while skin surfaces and subcutaneous tissue remain at lower and physiologic temperatures not harmful to living tissue. An electrode structure having a wall with an emitting surface adapted to be placed in direct facial contact or in close proximity with external skin surfaces, the wall forming part of a cooling chamber through which cooling fluid is circulated to maintain the wall and adjacent tissue at selected relatively cool temperature. The electrode wall is connected to a radio frequency generator through impedance matching circuitry. In one embodiment, the wall surface is suitably curved for direct uniform contact with the surface configuration of the body to which it is applied. In another example, one wall is made of a flexible, metallized material to serve as an electrode and to provide a surface closely conforming to external surface configuration of such body. In a further embodiment, the entire electrode is flexible -- the cooling chamber and metallized material both closely conform to external surface configuration of such body. In all examples, extended area cooling may be provided by additional or auxiliary cooling chamber peripheral to, and beyond, the electrode surface.