  We show that effective field theory techniques can be efficiently used to
compute power corrections to the hard thermal loops (HTL) in a high temperature
T expansion. To this aim, we use the recently proposed on-shell effective field
theory (OSEFT), which describes the quantum fluctuations around on-shell
degrees of freedom. We provide the OSEFT Lagrangian up to third order in the
energy expansion for QED, and use it for the computation of power corrections
to the retarded photon polarization tensor for soft external momenta. Here soft
denotes a scale of order $eT$, where $e$ is the gauge coupling constant. We
develop the necessary techniques to perform these computations, and study the
contributions to the polarization tensor proportional to $e^2 T^2$, $e^2 T$ and
$e^2 T^0$. The first one describes the HTL contribution, the second one
vanishes, while the third one provides corrections of order $e^2$ to the soft
photon propagation. We check that the results agree with the direct calculation
from QED, up to local pieces, as expected in an effective field theory.
