Near hyperthermic heater wound covering

An apparatus applies heat to tissue from a level that does not contact the tissue, in order to elevate the temperature of the tissue being treated toward normothermia. The apparatus may be attached to the skin of a person to form a treatment volume about the tissue to be treated. A heater, supported at the layer, is held near the tissue to be treated, out of contact with the tissue. The heater is for operating in a near-hyperthermic temperature range in order to treat the tissue. An example of a near-hyperthermic temperature range is 38° C. to 46° C. A controller may include means that cause the heater to operate over a therapeutic sequence, that cycle the heater on and off, that provide selectable average temperature values, that cause the heater to operate over an average temperature range, that cause the heater to operate at an average temperature over a therapy cycle, or that cause the heater to operate at an average temperature over a therapeutic sequence.