  We have used a Fourier Transform Spectrometer on the James Clerk Maxwell
Telescope to study the submillimetre continuum emission from dust in three hot
molecular cores (HMC). The spectral index beta of the dust emission for these
sources has been determined solely within the 30 GHz wide 350 GHz (850 micron)
passband to an accuracy comparable to those determined through multi-wavelength
observations. We find an average beta = 1.6, in agreement with spectral indices
determined from previous submillimetre observations of these sources and with
those determined for HMC in general. The largest single source of uncertainty
in these results is the variability of the atmosphere at 350 GHz, and with
better sky subtraction techniques we show that the dust spectral index can
clearly be determined within one passband to high accuracy with a submillimetre
FTS. Using an imaging FTS on SCUBA-2, the next generation wide-field
submillimetre camera currently under development to replace SCUBA at the JCMT
in 2006, we calculate that at 350 GHz it will be possible to determine beta to
+/- 0.1 for sources as faint as 400 mJy/beam and to +/- 0.3 for sources as
faint as 140 mJy/beam.
