Gaseous helium is being considered as a cryogen for a variety of high-power density applications. It is capable of reaching operational temperature levels as low as 20 K. This paper presents a time efficient method of designing and modeling a high-temperature superconducting dc cable. The analysis is an extension of a previously presented mathematical model in which the volume element method was used to characterize the fluid flow and heat transfer by conduction, convection, and radiation through a flexible cable cryostat. A system of ordinary differential equations was formulated using the fundamental principles of thermodynamics. The computational domain consists of volume elements distributed in three dimensions to account for the spatial dependence of the model. The pressure drop of the gaseous helium was calculated based on the Darcy-Weisbach correlation. Additionally, the temperature distribution was solved numerically using adaptive time-stepping. The obtained solutions converge within a timescale on the order of seconds to minutes, and the steady state results along with a transient analysis is discussed.