The transient temperature responses in a one-dimensional semitransparent slab with variable refractive index caused by a pulse irradiation are studied. The processes of the transient coupled radiative-conductive heat transfer in the semitransparent slab are analyzed numerically. An implicit central-difference scheme is employed for handling the energy equation, while a discrete curved ray-tracing method is used to solve the radiative transfer equation. The transient temperature responses in the case of constant refractive index are compared with those in the case of variable spatial refractive index. The results show that the spatial variation of refractive index has significant influences on the transient temperature responses of semitransparent slab. Omitting the spatial variation of refractive index may result in errors of transient temperature responses within semitransparent slab to some extent. The effects of optical thickness and refractive index gradient on the transient temperature responses are significant. Increasing the slab optical thickness, the effects of refractive index gradient on the transient temperature responses increase, especially for the non-incident surface.