  We investigate how much warm (T \sim 10^6 K) gas may exist in a Local Group
corona, and, in particular, whether such a corona could be detected indirectly
through its ionizing radiation. We calculate the non-LTE cooling of warm,
low-density gas and the resulting ionizing photon emissivities for a range of
metallicities. In principle a corona can produce a photon flux which
significantly exceeds the cosmic ionizing background. However, the additional
constraints which can be imposed on intragroup gas rule out models which
produce detectable ionizing photon fluxes at the Milky Way's distance from the
Local Group barycenter.
