Abstract: In general, the present invention incorporates a cooling or heating wrap having internal channels to circulate a chilled or warmed fluid, with one or more layers of a thermo-conductive material to eliminate air pockets or gaps between the wrap and a human or animal body part. The thermo-conductive material may be applied directly to the human or animal skin and/or body part, may be encapsulated in a separate unit, or may be integrated into the wrap itself. The thermo-conductive material acts like a heat conduction medium between the heat exchanging wrap and the anatomical body part, to increase the therapeutic effect of the wrap.