Energy-momentum tensor in thermal strong-field QED with unstable vacuum

The mean value of the one-loop energy-momentum tensor in thermal QED with electric-like background that creates particles from vacuum is calculated. The problem differes essentially from calculations of effective actions (similar to that of Heisenberg--Euler) in backgrounds that do not violate the stability of vacuum. The role of a constant electric background in the violation of both the stability of vacuum and the thermal character of particle distribution is investigated. Restrictions on the electric field and its duration under which one can neglect the back-reaction of created particles are established.