  A theoretical formulation for spin transport through an antiferromagnetic
(AF) insulator is presented in the case driven/detected by direct/inverse spin
Hall effect in two heavy metal contacts. The spin signal is shown to be
transferred by the ferromagnetic correlation function of the antiferromagnet,
which is calculated based on a magnon representation. To cover high temperature
regimes, we include an auxiliary field representing short AF correlations and a
temperature-dependent damping due to magnon scattering. The diffusion length
for spin is long close to the degeneracy of the two AF magnons, and has a
maximum as function of temperature near the N\'eel transition.
