  Using the cosmic virial theorem, Press-Schechter analysis and numerical
simulations, we compute the expected X-ray background (XRB) from the diffuse
IGM with the clumping factor expected from gravitational shock heating. The
predicted fluxes and temperatures are excluded from the observed XRB. The
predicted clumping can be reduced by entropy injection. The required energy is
computed from the two-point correlation function, as well as from
Press-Schechter formalisms. The minimal energy injection of 1 keV/nucleon
excludes radiative or gravitational heating as a primary energy source. We
argue that the intergalactic medium (IGM) must have been heated through violent
processes such as massive supernova bursts. If the heating proceeded through
supernova explosions, it likely proceeded in bursts which may be observable in
high redshift supernova searches. Within our model we reproduce the observed
cluster luminosity-temperature relation with energy injection of 1 keV/nucleon
if this injection is assumed to be uncorrelated with the local density. These
parameters predict that the diffuse IGM soft XRB has a temperature of ~1 keV
with a flux near 10 keV/cm^2 s str keV, which may be detectable in the near
future.
