It is commonly taken for granted that long time solutions of Cattaneo's
hyperbolic heat conduction equation tend to overlap the related
parabolic solutions. Usually, for short times considerable qualitative
as well as quantitative differences between the hyperbolic and parabolic
solutions are observed which vanish completely for long times. However,
in the case of a body with the internal heat source which capacity
depends on temperature the quantitative differences may grow with time.
This arises from the positive feedback between the source capacity and
the temperature. To illustrate this effect Cattaneo's hyperbolic
equation for the semi-infinite body with the heat source which capacity
is linearly dependent on temperature is solved analytically by the
Laplace transforms method.