  Correlators of magnetic and electric field energy density are investigated
for SU($N_c$) gauge theory at high temperatures $T$. At separations $z\leq 2/T$
the correlators are shown to be dominated by a power--law behavior even for
finite gluon screening masses. This continuum behavior is well approximated on
current $4\times 16^3$--lattices in the perturbative limit and leads to a
considerable overestimate of screening masses deduced from fitting the lattice
correlators with conventional exponential forms. The use of extended sources
and sinks to enhance the signal improves the situation for screening masses
$m\gg T$ but leads to a largely uncontrolled error for masses less than $T$. In
fact, we show that recent lattice QCD data of Grossmann et al., from which a
magnetic screening mass $m_M \approx 2.9 \, T$ was deduced, may even be
consistent with a vanishing actual magnetic screening mass.
