Thermal wave propagation in an infinite solid medium which surrounds an infinitely long cylindrical surface is considered. This surface transfers a prescribed and time-dependent heat flux to the solid medium. The non-stationary heat conduction problem is studied by assuming a non-vanishing value of the thermal relaxation time for the solid medium, i.e. by employing the hyperbolic heat conduction equation. An analytical expression of the temperature field in the solid is determined. Examples are provided for heat fluxes which vary with lime as a square wave pulse or as a triangular wave pulse. Comparisons with the solutions obtained for parabolic heat conduction are performed.