  We report on the computation of a class of massless bosonic three-loop vacuum
sum-integrals which are key building blocks for an evaluation of the Debye
screening mass in hot QCD. Generalizing known techniques and introducing the
concept of tensor reduction by dimensionality shifts (known to the
zero-temperature community since the work of Tarasov in 1996) to finite
temperature, we are able to treat hitherto unaccessible cases, which will allow
us to finalize the long-term project of NNLO Debye mass evaluation.
