  The damping rate \gamma_t(p) of on-shell transverse gluons with ultrasoft
momentum p is calculated in the context of next-to-leading-order
hard-thermal-loop-summed perturbation of high-temperature QCD. It is obtained
in an expansion to second order in p. The first coefficient is recovered but
that of order p^2 is found divergent in the infrared. Divergences from
light-like momenta do also occur but are circumvented. Our result and method
are critically discussed, particularly regarding a Ward identity obtained in
the literature. When enforcing the equality between \gamma_t(0) and
\gamma_l(0), a rough estimate of the magnetic mass is obtained. Carrying a
similar calculation in the context of scalar quantum electrodynamics shows that
the early ultrasoft-momentum expansion we make has little to do with the
infrared sensitivity of the result.
