  Constant temporal backgrounds have become a convenient tool for the
discussion of continuum non-abelian gauge theories at finite temperature, as
they provide a grasp on the confinement/deconfinement transition. It has been
pointed that such backgrounds are better dealt with within so-called
Cartan-Weyl color bases, rather than within the standard Cartesian bases. Here,
we discuss the specificities of the evaluation of SU($N$) color factors within
these bases, extending the discussion in Ref. [1].
