A heat exchange module alone or part of a system including a control console. The module includes a channel assembly and a heat exchange stack attached thereto, and can be used to directly cool and/or heat tissue or skin. The channel assembly includes a liquid channel. The stack can include a pair of spaced plates with thermoelectric coolers exchangers, heat reflective layers, and a core composite layer which keeps the plates spaced. To provide flexibility of the module to better fit on round body parts the stack can include a thermally-conductive plate construction between the plates which has rotational flexibility axes in the X and/or Y directions between plate portions. Optionally the channel can include windows to which the plate portions are sealed. The heat exchange stack separately or together with the channel assembly can be secured in the thickness direction with mechanical securements such as sewing or tacking to also provide for greater flexibility.
