  On the lattice we study the gauge boson propagator of three dimensional
compact QED in Landau gauge at zero and non-zero temperature. The
non-perturbative effects are taken into account by the generation of a mass, by
an anomalous dimension and by the photon wave function renormalization. All
these effects can be attributed to the monopoles: they are absent in the
propagator of the singularity-free part of the gauge field. We assess carefully
the Gribov copy problem for the propagator and the parameters emerging from the
fits.
