A heat exchange module to thermally treat body tissue of a subject, comprising: a fluid channel assembly including a channel, an inlet and an outlet; a heat exchange stack attached to the channel assembly; wherein said channel has a plurality of window openings configured to expose the interior of said channel; the heat exchange stack including thermoelectric coolers; the heat exchange stack including a thermally-conductive plate construction configured to provide flexibility for the channel assembly and thereby for the heat exchange module; wherein the thermally conductive plate construction of the heat exchange stack includes thermally conductive plate pieces which are attached to seal each of said plurality of window openings to allow for sufficient transfer of heat into said channel; a first heat reflective layer disposed over said thermally conductive plate pieces and said channel assembly, said first heat reflective layer having window cutouts through which each of said thermoelectric coolers pass to make thermal contact with one of said thermally conductive plate pieces; a core composite layer disposed over said first heat reflective layer, wherein said core composite layer is configured with windows so that said core composite layer surrounds each of said thermoelectric coolers to provide interstitial insulation; a second heat reflective layer disposed over said core composite layer, said second heat reflective layer having window cutouts for each of said thermoelectric coolers; a thermally conductive top plate disposed over said second heat reflective layer and configured to make contact with said thermoelectric coolers; wherein a combination of said first heat reflective layer and said second heat reflective layer is configured to prevent heat from radiating between said thermally conductive plate pieces and said thermally conductive top plate by reflecting emitted radiation back to the plate from which it originates; and a thermally conductive biocompatible layer disposed over said top plate, said biocompatible layer configured to act as a buffer between said thermally conductive top plate and body tissue to which said heat exchange module is applied. a fluid channel assembly including a channel, an inlet and an outlet; a heat exchange stack attached to the channel assembly; wherein said channel has a plurality of window openings configured to expose the interior of said channel; the heat exchange stack including thermoelectric coolers; the heat exchange stack including a thermally-conductive plate construction configured to provide flexibility for the channel assembly and thereby for the heat exchange module; wherein the thermally conductive plate construction of the heat exchange stack includes thermally conductive plate pieces which are attached to seal each of said plurality of window openings to allow for sufficient transfer of heat into said channel; a first heat reflective layer disposed over said thermally conductive plate pieces and said channel assembly, said first heat reflective layer having window cutouts through which each of said thermoelectric coolers pass to make thermal contact with one of said thermally conductive plate pieces; a core composite layer disposed over said first heat reflective layer, wherein said core composite layer is configured with windows so that said core composite layer surrounds each of said thermoelectric coolers to provide interstitial insulation; a second heat reflective layer disposed over said core composite layer, said second heat reflective layer having window cutouts for each of said thermoelectric coolers; a thermally conductive top plate disposed over said second heat reflective layer and configured to make contact with said thermoelectric coolers; wherein a combination of said first heat reflective layer and said second heat reflective layer is configured to prevent heat from radiating between said thermally conductive plate pieces and said thermally conductive top plate by reflecting emitted radiation back to the plate from which it originates; and a thermally conductive biocompatible layer disposed over said top plate, said biocompatible layer configured to act as a buffer between said thermally conductive top plate and body tissue to which said heat exchange module is applied.