  Time evolution of tunneling phenomena proceeding in thermal medium is studied
using a standard model of environment interaction. A semiclassical probability
formula for the particle motion in a metastable state of one dimensional system
put in thermal medium is combined with the formula of quantum penetration
factor through a potential barrier, to derive the tunneling rate in medium.
Effect of environment, its influence on time evolution in particular, is
clarified in a real-time formalism. A nonlinear resonance effect is shown to
enhance the tunneling rate at finite times of order $2/\eta $, with $\eta $ the
friction coefficient. In the linear approximation this effect has relevance to
the parametric resonance. This effect enhances the possibility of early
termination of the cosmological phase transition much prior to the typical
Hubble time.
