This paper deals with an inverse asymmetric transient thermoelastic problem of a composite hollow cylinder consisting of an inner structural layer and an outer piezoelectric layer. It is assumed that an unknown transient heating temperature distribution acts on the inside surface of the hollow cylinder and an induced transient electric potential distribution is measured on the outside surface. This inverse thermoelastic problem is analyzed by employing the finite difference method with respect to a time variable and the unknown heating temperature is inferred from the measured electric potential distribution. The numerical results obtained for a composite hollow cylinder made with a stainless steel layer and a cadmium selenide layer are shown in a graphical form.