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.