A relaxation model for heat conduction and generation is presented which
takes into account the finite velocity of heat propagation and the inertia
of the internal heat source. Special attention is given to the effect
of the source terms in the newly formulated heat conduction equation
on the temperature field. The novel heat conduction equation is transformed
into a dimiensionless form and its special cases are considered. Several
initial value problems are solved analytically for a zero-dimensional case
of heat conduction and generation. It is observed that, unlike the
classical hyperbolic model, the relaxation solutions generally do not tend to
approach the corresponding parabolic solutions.