  We consider the Cauchy problem for the heat diffusion equation in the whole
Euclidean space consisting of two media with different constant conductivities.
The large time behavior of temperature, the solution of the problem, is studied
when initially temperature is assigned to be 0 on one medium and $1$ on the
other. We show that under a certain geometric condition of the configuration of
the media, temperature is stabilized to a constant as time tends to infinity.
We also show by examples that temperature in general oscillates and is not
stabilized.
