Fred Hoyle is known as creator of the so-called “steady state universe” which latter, although permanently expanding,
does not change its state of matter, especially keeping its density constant. To achieve this virtue Hoyle introduced
into the energy-momentum tensor of the GRT field equations a term derived from a so-called ad-hoc creation field
astonishingly leading to field equations very similar to the ones already developed by Tolman when introducing
energy sources connected with viscous dissipation forces acting upon dust-like cosmic matter [1]. In this article here
we shall again study the action of viscous forces in cosmic baryonic matter and shall boil it down to volume viscosity
contributions to the viscous stress tensor in a universe with a compressible Hubble flow. Assuming that by collisions
of any kind the energy of the differential Hubble drift between two collision points of cosmic matter particles, seen
in the non-inertial rest frames of moving particles, is randomized and converted into thermal energy, one can then
show with the help of a kinetic transport equation that during the cosmic expansion permanently thermal energy is
generated leading to the result that the matter temperature, instead of falling-off, is linearly increasing with the scale
of the universe. This not only questions the standard use of the model of pressure-free, dust-like matter in the universe,
but furthermore indicates the possibility of an asymptotic cosmic-ray-like matter state including the possibility of
matter creation by pair production.