  Time evolution of quantum tunneling is studied when the tunneling system is
immersed in thermal medium. We analyze in detail the behavior of the system
after integrating out the environment. Exact result for the inverted harmonic
oscillator of the tunneling potential is derived and the barrier penetration
factor is explicitly worked out as a function of time. Quantum mechanical
formula without environment is modifed both by the potential renormalization
effect and by a dynamical factor which may appreciably differ from the
previously obtained one in the time range of 1/(curvature at the top of
potential barrier).
