  We investigate the finite-temperature excitation spectrum in the gluon sector
of $SU(3)$ pure gauge theory through measurements of screening masses in
correlations of loop operators. We develop the classification of such operators
under the symmetry group of the `$z$-slice'. In the confined phase of the
theory, we find that the spectrum dynamically realises the zero temperature
symmetries. We observe a large thermal shift of the $0^{++}$ glueball mass. In
the deconfined phase, the spectrum distinguishes between operators coupling to
electrically and magnetically polarised gluon fields. The former yields a
screening mass equal to the Wilson-line screening mass; the latter, a method
for the measurement of the magnetic mass in the high-temperature limit.
