The interaction of natural convection with thermal radiation affects the transient response of a plate fin; this is studied analytically. The Rosseland approximation is applied to describe radiative heat transfer in the flow boundary layer. A cubic spline colocation method is used to perform the numerical computation. The important parameters of the problem are the aspect ratio, the convection-conduction parameter, and the radiation-conduction parameter. The results indicate that the time taken for the fin root to reach the specified temperature is almost independent of aspect ratio at large heat input. The surface heat flux is affected to a large extent by the convection-conduction parameter. The surface heat transfer rate increases with increasing radiative interaction. At large heat input, the temperature distribution at the base of the fin is nearly isothermal.