A miniature mixed gas refrigeration system is disclosed, having a coaxial catheter (18) with an inner high pressure supply lumen (24) and an outer low pressure return lumen (22). The gas mixture is pressurized by a compressor (12) to a pressure less than 420 psia, for safety reasons. The distal portion (23) of the outer lumen contains a micro-miniature heat exchanger (28) constructed of laminated plates or sheets (42). The plates or sheets (42) establish high pressure (36) and low pressure passageways (40), with high surface area, having a tortuous path for the gas flow to maximize heat exchange. The high pressure outlet (50) of the heat exchanger (28) is connected to a Joule-Thomson expansion element (30) where the high pressure gas is expanded isenthalpically to a lower temperature at least as low as 180K. This low temperature gas cools a heat transfer element (32) mounted in the outer wall of the catheter, to cool an external object. Return gas flows back through the heat exchanger to pre-cool the incoming high pressure gas mixture.