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.