Future superconduction radio frequency (SRF) cavities, as part of Project X at Fermilab,will be cooled to superfluid helium temperatures by a cryogenic distribution system supplying cold supercritical helium. To reduce vapor fraction during the final Joule Thomson (J-T) expansion into the superfluid helium cooling bath, counter-flow, plate-fin heat exchanger are an effective option. However, at liquid helium temperatures requires consideration of axial heat conduction along the direction of flow, in addition to variable fluid properties. Here we present a numberical model that includes the effects of axial guide design decisions on heat exhanger material choice and geometry. In addition, the J-T expansion process is modeled with the heat exchanger to analyze the effect of heat load and cryogenic supply parameters.