Observing high-temperature, low emission measure plasma is key to unlocking the coronal heating problem. With current instrumentation, a combination of EUV spectral data from Hinode Extreme-ultraviolet Imaging Spectrometer (EIS; sensitive to temperatures up to 4 MK) and broadband filter data from Hinode X-ray Telescope (XRT; sensitive to higher temperatures) is typically used to diagnose the temperature structure of the observed plasma. In this Letter, we demonstrate that a "blind spot" exists in temperature-emission measure space for combined Hinode EIS and XRT observations. For a typical active region core with significant emission at 3-4 MK, Hinode EIS and XRT are insensitive to plasma with temperatures greater than ~6 MK and emission measures less than ~1027 cm-5. We then demonstrate that the temperature and emission measure limits of this blind spot depend upon the temperature distribution of the plasma along the line of sight by considering a hypothetical emission measure distribution sharply peaked at 1 MK. For this emission measure distribution, we find that EIS and XRT are insensitive to plasma with emission measures less than ~1026 cm-5. We suggest that a spatially and spectrally resolved 6-24 Å spectrum would improve the sensitivity to these high-temperature, low emission measure plasma.