  We consider induced pair production in an external field at finite
temperature. One-loop correction to the Green function of a meson is calculated
semiclassically within the framework of saddle-point analysis of Schwinger
proper time integrals. This correction appears to be exponentially small in
terms of inverse temperature dependence. Low-temperature limit is shown to be
in full agreement with previously obtained zero-temperature results. The
corrections in the low-temperature limits are estimated up to the leading
exponential and pre-exponential terms. Comparison is made to earlier
calculations of vacuum decay.
