A procedure for analyzing low-energy (≲100 eV) ion data from the plasma composition experiment on ISEE 1 is presented and examined in detail. The method is based on a derived analytic expression for particle flux to a limited aperture RPA in the thin sheath approximation, which takes into account some effects of a charged spacecraft on plasma particle trajectories. Calculations using simulated data are employed to test the efficacy and accuracy of the technique. On the basis of the analysis of these calculation results and the mathematical model, it appears that the method can generally be expected to provide accurate ion temperatures from all good plasmaspheric RPA data. Corresponding densities and spacecraft potentials should be accurate when spacecraft potentials are negative but are subject to error for positive spacecraft potentials, particularly when ion Mach numbers are low (≪1). Beyond the plasmasphere, the method is applicable only in special circumstances. Analysis of data from a representative ISEE 1 pass results in a plasmasphere temperature profile consistent in overall structure with previous observations.