  We calculate thermal corrections to the non-linear QED effective action for
low-energy photon interactions in a background electromagnetic field. The
high-temperature expansion shows that at $T \gg m$ the vacuum contribution is
exactly cancelled to all orders in the external field except for a non-trivial
two-point function contribution. The high-temperature expansion derived reveals
a remarkable cancellation of infrared sensitive contributions. As a result
photon-splitting in the presence of a magnetic field is suppressed in the
presence of an electron-positron QED-plasma at very high temperatures. In a
cold and dense plasma a similar suppression takes place. At the same time
Compton scattering dominates for weak fields and the suppression is rarely
important in physical situations.
