The conditions for the manifestation of transient effects in fission are carefully examined by analysing experimental data where fission is induced by peripheral heavy-ion collisions at relativistic energies. Experimental total nuclear fission cross sections of $^{238}$U at 1 A GeV on gold and uranium targets are compared with the predictions of a nuclear-reaction code, where transient effects in fission are modeled using different approximations to the numerical time-dependent fission-decay width: a new analytical description based on the solution of the Fokker–Planck equation and two widely used but less realistic descriptions, a step function and an exponential-like function. The experimental data are only reproduced when dissipation is considered. The influence of transient effects on the fission process, as well as the deduced value of the dissipation strength β, depends strongly on the approximation applied for the time-dependent fission-decay width. In particular, a meticulous analysis sheds severe doubts on the use of the exponential-like in-growth function. Finally, we investigate which should be the characteristics of experimental observables to be most sensitive to transient effects in fission. The pertinence of observables related to the excitation energy at saddle is discussed.Read less <