A flexible mesoscopic heat exchanger is provided by the invention. The heat exchanger of the invention includes uniform microchannels for fluid flow. Separate header and channel layers include microchannels for fluid flow and heat exchange. A layered structure with channels aligned in multiple orientations in the layers permits the use of a flexible material without channel sagging and provides uniform flows. In a preferred embodiment, layers are heat sealed, e.g., by a preferred lamination fabrication process.