[en] Computer programs were written to design and simulate the behavior of three heat exchangers for cooling supercritical helium to approximately 4.3⁰K at 4 atm. Helium, at 1, 3, or 5 gm/sec, is cooled by passing it through 0.635-cm-diam copper tubing immersed in a liquid nitrogen bath, through a copper, concentric tube, counter-current heat exchanger, and then through 0.635-cm copper tubing immersed in a liquid helium bath. The helium then enters a superconducting test magnet and finally passes through the annulus of the countercurrent exchanger before venting to the atmosphere. Several acceptable designs are presented that meet design and space limitations