Temperature and the emission measure data are obtained by the filter ratio method from images of the coronal helmet streamer observed by the Yohkoh Soft X-Ray Telescope (SXT) on 1992 January 24. Two averaging procedures are used for the results enhancement: the median filtering and the latitudinal averaging over a small heliocentric arc. The plasma density and temperature in the closed field region are calculated from the data, under the assumption that the line-of-sight depth of the structure is constant. The results are then compared with the thermodynamic equilibrium model. Significant deviations of the calculated pressure from the thermodynamic equilibrium are found at the top of the helmet. The proposed geometrical model of the helmet that takes into account possible variations in the line-of-sight depth of the structure explains the discrepancy between the data and the equilibrium model.