This numerical study of the global distribution of helium in the terrestrial thermosphere is based on the extension of a three-dimensional single-fluid numerical model of the thermosphere previously developed by the authors to treat the dynamics of a minor gas imbedded in a background gas made up to N2, O2, and O. The Cira (1972) model of the upper atmosphere, based on satellite drag data is used to specify the background gas density and temperature as functions of altitude, and local time for a given day of the year. Specific emphasis is placed on a study of the helium distribution at solstice, i.e., the 'winter helium bulge.' Effects of solar activity, eddy diffusion, and exospheric transport on the global distribution of helium are investigated. The model reproduces the general features of the winter helium bulge, including the variation of its amplitude with solar activity, as determined by comparison of data from several recent satellite-borne mass spectrometers.