  The electron-positron `box' diagram produces an effective action which is
fourth order in the electromagnetic field. We examine the behaviour of this
effective action at high-temperature (in analytically continued imaginary-time
thermal perturbation theory). We argue that there is a finite, nonzero limit as
$T\rightarrow \infty$ (where $T$ is the temperature). We calculate this limit
in the nonrelativistic static case, and in the long-wavelength limit. We also
briefly discuss the self-energy in 2-dimensional QED, which is similar in some
respects.
