  In the paper the quantum hyperbolic equation formulated in [M. Kozlowski, J.
Marciak-Kozlowska, From Quarks to Bulk Matter, Hadronic Press, 2001], is appled
to the study of the propagation of the initial thermal state of the Universe.
It is shown that the propagation depends on the barrier height. The Planck wall
potential is introduced, V_P=hbar/8t_P=1.25 10^18 GeV where t_P is a Planck
time. For the barrier height V<V_P the master thermal equation is the modified
Klein-Gordon equation and for barrier height V>V_P the master equation is the
Klein-Gordon equation. The solutions of both type equations for Cauchy boundary
conditions are discussed.
