The operational restrictions on several current interferometer/radiometer instruments are such that focal planes, optical components, and telescope baffles must be maintained at temperatures near 8°K, 20°K, and 80°K respectively. One reliable method of achieving this is to expel supercritical helium from a supply dewar at constant pressure by applying energy to a dewar heater; the resulting flow then passes serially through three (or more) heat exchangers to achieve the desired cooling before being vented through a pressure regulator valve. A convenient set of approximate, time-dependent equations that can be programmed on a hand-held calculator for the preliminary design of a supercritical helium cooling system are presented in this paper. Predicted temperature and mass flow rates based on the simplified equations agree within 5 percent of those resulting from analyses by other researchers. The equations are applied to a particular cooler system for the CIRRIS 82 instrument scheduled to be flown on the Space Shuttle in 1982.