  We use RHESSI high-resolution imaging and spectroscopy observations from ~6
to 100 keV to determine the statistical relationships between measured
parameters (temperature, emission measure, etc.) of hot, thermal plasma in 37
intense (GOES M- and X-class) solar flares. The RHESSI data, most sensitive to
the hottest flare plasmas, reveal a strong correlation between the maximum
achieved temperature and the flare GOES class, such that "super-hot"
temperatures >30 MK are achieved almost exclusively by X-class events; the
observed correlation differs significantly from that of GOES-derived
temperatures, and from previous studies. A nearly-ubiquitous association with
high emission measures, electron densities, and instantaneous thermal energies
suggests that super-hot plasmas are physically distinct from cooler, ~10-20 MK
GOES plasmas, and that they require substantially greater energy input during
the flare. High thermal energy densities suggest that super-hot flares require
strong coronal magnetic fields, exceeding ~100 G, and that both the plasma
{\beta} and volume filling factor f cannot be much less than unity in the
super-hot region.
