  The physical characteristics of the Lyman-alpha forest cloud systems are
combined with observations on the baryonic mass density of the Universe and
constraints from primordial nucleosynthesis to set boundary conditions on the
Intergalactic Medium (IGM) at the epoch of z=2.5. The Universe is considered a
closed system and allowed to expand adiabatically from the epoch when QSOs
first ionized the IGM (5 <= z_on <= 20). The average kinetic energy of a gas is
calculated in the region where the gas transitions from relativistic to
non-relativistic behavior. All of the above measurements are then used to
determine the thermal history of the IGM in the redshift range 2.5 <= z <=
z_on. The hot IGM is assumed to inverse Compton scatter photons from the Cosmic
Microwave Background (CMBR) and consequently distort the CMBR as seen at the
present epoch. The temperature of the IGM at z=2.5 and the epoch z_on are
adjusted, within the constraints defined above, to give the best overall
agreement with published data on the temperature of the IGM. We find that the
model of the IGM proposed here does not grossly distort the CMBR, and in fact
agrees quite closely with the preliminary results from the Cosmic Background
Explorer (COBE) satellite. However, our model of the IGM cannot explain the
observed cosmic x ray background.
  This paper was originally written in 1990. It was never submitted for
publication.
