Using a magnetic mirror plasma device, helium ion temperatures were investigated using high resolution Doppler spectroscopy of the He II line at 468.6 nm. The objective was to improve the quality of fits to Langmuir probe data. Measured temperatures, which represent an average value over a line of sight, ranged from 0.07 eV to 0.32 eV with higher values reached in stronger magnetic fields. An analytic expression for the line of sight integral of a variable width Gaussian signal is presented, and it is demonstrated that the integrated signal can, in practice, be accurately fitted by a single Gaussian line shape. A large number of spectra was acquired using a randomized experimental design with four independently controllable engineering variables and three discrete magnetic fields. Separate parameterizations of the results for each magnetic field in terms of the engineering variables showed that the data could already be well fitted using only the plasma current as a predictor. The fit to the ion temperature data was significantly improved when both the plasma current and filament bias voltage were used as predictors. The helium gas fill pressure had negligible predictive value for the ion temperature. (figures in this article are in colour only in the electronic version).