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A linear hyperbolic heat conduction model based on the modified Fourier Law is developed for a composite region. The investigation of thermal waves in composites has become important in light of some recent experimental results showing the existence of reflections at the interfaces in dissimilar mediums. In the temperature variable, a new and nonseparable boundary condition is obtained at the interface of the regions. Unlike classical parabolic heat conduction, the field equations also become nonseparable in this new formulation and thus cannot be solved by standard techniques. However, a generalized finite integral transform technique is developed in the flux domain and is applied to the case of a two region slab with a step change in temperature at one outside surface. This generalized finite integral transform technique leads to an infinite set of ordinary differential equations for the transform. These equations are transformed into an infinite set of linear Volterra integral equations of the second kind. The Method of Bownds is then used to obtain numerical results for the integral transforms. These values are used to show the unusual behavior of the heat flux and temperature distributions resulting from a hyperbolic heat conduction model in a composite. The results show that when a thermal wave encounters an interface between dissimilar materials, a portion of the energy is reflected while the rest Is transmitted. Also the speed of propagation may change as a thermal wave penetrates into a region of different thermal properties.