We characterize the soft X ray solar corona in terms of the physical parameters of density and temperature derived from the Soft X ray Telescope on board the Yohkoh satellite for the period of solar minimum covered by the Whole Sun Month coordinated campaign. In particular, we concentrate on August 18, 1996, a day with no major active regions on the solar disk, to provide data for comparison with other instruments taking part in this campaign. The density is found to decrease with height along all radial lines in the solar corona. These radial lines span a number of distinct structures, including a well-defined helmet streamer in the northwest quadrant. The radial variation of the temperature is far more complex, displaying a variety of forms. To provide a theoretical context for these observations, we investigate two distinctly different heating models. For regions of the corona in which the temperature increases with height we apply an inward heat flux model to describe the heating. A mechanical energy flux model is assumed to heat the coronal regions in which the temperature displays a maximum at a given height. For each of the models discussed, the results are consistent with those found in previous studies of a similar nature. ¿ 1999 American Geophysical Union