  The contribution of Lorentz non-scalar operators to finite temperature
correlation functions is discussed. Using the local duality approach for the
one-pion matrix element of a product of two vector currents, the temperature
dependence of the average gluonic stress tensor is estimated in the chiral
limit to be $\langle{\bf E}^2 +{\bf B}^2\rangle_{T}=\frac{\pi^2}{10}bT^4$. At a
normalization point $\mu=0.5$ GeV we obtain $b\approx 1.1$. Together with the
known temperature dependence of the Lorentz scalar gluon condensate we are able
to infer $\langle{\bf E}^2\rangle_T$ and $\langle{\bf B}^2\rangle_T$ separately
in the low-temperature hadronic phase.
