The hyperfine pressure shift (HPS) of hydrogen atoms in a helium atmosphere is calculated over a wide temperature range (50-700°K). Results are not very sensitive to the exact form of the H-He potential, but depend strongly on the values of the spin density at the hydrogen nucleus at different H-He interatomic separations. Spin densities are evaluated by the spin-optimized self-consistent-field (SOSCF) method and are corrected for the long-range Van der Waals interaction. It is argued that long-range spin density shifts are indeed negative as suggested by several previous calculations, in contrast with a recent five-configuration treatment. Our results are 20%-25% higher than experimental values. Most of the error is attributed to the uncertainties concerning the method of including long-range effects.