Heat treatment is applied to tissue in need of such treatment which is surrounded by tissue not in need of such treatment, by positioning a deposit within the surrounding tissue adjacent the tissue in need of treatment. The dielectric constant and/or the conductivity of the deposit is greater than that of the surrounding tissue. A radio frequency antenna or antenna array directs a radio frequency signal at a selected frequency into the deposit. The deposit has a diameter within a range of about 0.5 times to about 0.16 times the wavelength of the radio frequency signal within the surrounding tissue. The deposit is heated, at least partially through resonant heating, to a temperature greater than the surrounding tissue to apply heat treatment to the tissue in need of treatment. The deposit may take the form of a balloon of a Mammosite.RTM. type device to provide hyperthermia treatment in conjunction with radiation treatment of a breast after a lumpectomy.