We have performed a differential emission measure (DEM) analysis for a polar coronal hole observed during solar minimum in 2007. Five observations are analyzed spanning the coronal hole from the central meridian to the boundary with the quiet-Sun corona. The observed heights ranged from 1.05 to 1.20 R sun. The analysis shows that the plasma is not strictly isothermal anywhere, but rather has a high-temperature component that extends up to log T(K) = 6.2-6.3. The size and importance of this component depend on location, and its evolving magnitude with height marks the boundary between the coronal hole and the quiet corona, where it becomes dominant. The DEM of the coronal hole plasma below log T(K) = 6.0 decreases faster with height than that of the high-temperature component. We discuss the possible nature of the high-temperature component. Our results highlight the potential limitations of isothermal analyses. Such methods actually measure a DEM-weighted average temperature and as a result can infer artificial temperature gradients. Assuming the gas is isothermal along the line of sight can also yield incorrect electron densities. By revealing structures along the line of sight, a DEM analysis can also be used to more reliably interpret electron temperature and density measurements.