  A simple model for a hot Local Group halo is constructed, using the standard
beta-model for the halo density and by choosing model parameters based on all
available observations of X-ray emission in other groups of galaxies and on
optical data on Local Group morphology. From the predicted X-ray intensities,
total Local Group mass, and central cooling time of the halo, we derive very
conservative upper limits on the central halo density N_0 and global
temperature T of N_0 = 5e-4 cm-3 and kT = 0.5 keV, irrespective of realistic
values of the density profile parameters r_c and beta. A typical poor group
value of beta = 0.5 requires kT < 0.15 keV and N_0 < 1e-4 cm-3, from which it
is concluded that the Local Group is very unlikely to possess a significant
X-ray halo. The prospects for further constraining of halo parameters from UV
absorption line observations are considered. We explicitly calculate the
ability of the halo to distort the cosmic microwave background (CMB) in terms
of the resulting CMB temperature variations and multipole anisotropies.
