A method for the hyperthermia treatment of tissue in a target site applies a heat source to kill cells without protein denaturization. The method introduces an encapsulated dye that is released at a selected temperature in the target site to indicate that a threshold temperature has been reached to hyperthermally treat the tissue. In one embodiment, the composition releases the dye at a temperature of 42.degree. C. to 50.degree. C., and preferably about 45.degree. C. to 49.degree. C. The composition which can be a liposome composition encapsulating the dye can be introduced to the bloodstream of the patient to flow through the target site.