The transient temperature distribution in a multilayer composite, semitransparent or transparent, absorbing and emitting medium that is suddenly exposed to a thermal radiative flux is investigated. Effects of both thermal radiation and conduction within each layer and convection on both exterior surfaces of the composite wall are considered. The internal heal generation from an electrically conductive thin-film heater is also considered. An analytic relation for obtaining the radiative flux in the multilayer stack is presented. Transient temperature solutions are obtained by a hybrid numerical algorithm. Illustrative solutions are presented for the transient surface temperature of a multilayer transparent medium after exposure to a very high radiative flux. Various surface reflectivities are examined.