  Electric fields may decay by quantum tunneling: as calculated by Schwinger,
an electron-positron pair may be summoned from the vacuum. In this paper I
calculate the pair-production rate at nonzero temperatures. I find that at high
temperatures the decay rate is dominated by a new instanton that involves both
thermal fluctuation and quantum tunneling; this decay is exponentially faster
than the rate in the literature. I also calculate the decay rate when the
electric field wraps a compact circle (at zero temperature). The same new
instanton also governs this rate: I find that for small circles decay is
dominated by a process that drops the electric field by one unit, but does not
produce charged particles.
