  The fundamental solution describing non-stationary elastic wave scattering on
an isotopic defect in a one-dimensional harmonic chain is obtained in an
asymptotic form. The chain is subjected to unit impulse point loading applied
to a particle far enough from the defect. The solution is a large time
asymptotics at a moving point of observation, and it is in excellent agreement
with the corresponding numerical calculations. At the next step, we assume that
the applied point impulse excitation has random amplitude. This allows one to
model the heat transport in the chain and across the defect as the transport of
the mathematical expectation for the kinetic energy and to use the conception
of the kinetic temperature. To provide a simplified continuum description for
this process, we separate the slow in time component of the kinetic
temperature. This quantity can be calculated using the asymptotics of the
fundamental solution for the deterministic problem. We demonstrate that there
is a thermal shadow behind the defect: the order of vanishing for the slow
temperature is larger for the particles behind the defect than for the
particles between the loading and the defect. The presence of the thermal
shadow is related to a non-stationary wave phenomenon, which we call the
anti-localization of non-stationary waves. Due to the presence of the shadow,
the continuum slow kinetic temperature has a jump discontinuity at the defect.
Thus, the system under consideration can be a simple model for the
non-stationary phenomenon, analogous to one characterized by the Kapitza
thermal resistance. Finally, we analytically calculate the non-stationary
transmission function, which describes the distortion (caused by the defect) of
the slow kinetic temperature profile at a far zone behind the defect.
