A heat exchanger module (HEM) and system uses a flexible substrate with one or more open channels, to which a substrate cover is bonded, thereby forming closed channels in the flexible substrate. Thermoelectric coolers (TECs) are attached to optional thermally diffusing copper squares atop the substrate cover. An interface cover is attached to the TEC tops, with a compliant thermally conductive material opposite the TECs and ultimately in contact with a patient. A liquid is passed through the closed channels, which act as thermal references for the TECs. Current is supplied by a controller to the TECs to induce TEC cooling or heating relative to the liquid. One or more temperature sensors detect the temperature of the interface cover, which are used as inputs to the control of the TEC supply current. The HEM may be used for heating, cooling, or cycling between heating and cooling for various medical uses.