  Statistical uncertainties in determining the temperatures of hot (0.5 keV to
10 keV) coronal plasmas are investigated. The statistical precision of various
spectral temperature diagnostics is established by analyzing synthetic ASCA
Solid-state Imaging Spectrometer (SIS) CCD spectra. The diagnostics considered
are the ratio of hydrogen-like to helium-like line complexes of $Z\ge14$
elements, line-free portions of the continuum, and the entire spectrum. While
fits to the entire spectrum yield the highest statistical precision, it is
argued that fits to the line-free continuum are less susceptible to atomic data
uncertainties but lead to a modest increase in statistical uncertainty over
full spectral fits. Temperatures deduced from line ratios can have similar
accuracy but only over a narrow range of temperatures. Convenient estimates of
statistical accuracies for the various temperature diagnostics are provided
which may be used in planning ASCA SIS observations.
