We analyze the temperature and EUV line emission of a coronal cavity and surrounding streamer in terms of a morphological forward model. We use a series of iron line ratios observed with the Hinode Extreme-ultraviolet Imaging Spectrograph (EIS) on 2007 August 9 to constrain temperature as a function of altitude in a morphological forward model of the streamer and cavity. We also compare model predictions to the EIS EUV line intensities and polarized brightness (pB) data from the Mauna Loa Solar Observatory (MLSO) Mark 4 K-coronameter. This work builds on earlier analysis using the same model to determine geometry of and density in the same cavity and streamer. The fit to the data with altitude-dependent temperature profiles indicates that both the streamer and cavity have temperatures in the range 1.4-1.7 MK. However, the cavity exhibits substantial substructure such that the altitude-dependent temperature profile is not sufficient to completely model conditions in the cavity. Coronal prominence cavities are structured by magnetism so clues to this structure are to be found in their plasma properties. These temperature substructures are likely related to structures in the cavity magnetic field. Furthermore, we find that the model overestimates the EUV line intensities by a factor of 4-10, without overestimating pB. We discuss this difference in terms of filling factors and uncertainties in density diagnostics and elemental abundances.