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We consider a rigid heat conductor characterized by two relaxation times and derive a linear hyperbolic equation for the temperature which can properly describe heat waves. The wave splitting technique is applied to the propagation problem whose solution is expressed in the form of the Laplace transform of the wave propagator. The reflectivity of a heat pulse is then obtained at an interface between two different conductors. Explicit results for both the propagation and the reflection problems are worked out under suitable conditions which allow for a second sound propagation in low temperature rigid conductors. The characteristic relaxation times of a reflecting conductor are also determined as the solution of an inverse reflection problem.