In rheological characterization of polymeric materials, the time–temperature superposition (TTS) principle allows us to acquire a wider spectrum of information on polymer dynamics. Although there are reports of the failure of TTS when both chain dynamics and local segmental dynamics are accessible at each of several temperatures, we have assumed that TTS would apply to describe the temperature dependence of transient responses of entangled melts to fast startup deformation. In this work we show that at the same effective rate (e.g., the same Rouse–Weissenberg number WiR equal to the product of the Hencky rate and the Rouse time) of uniaxial extension the nonlinear responses of several polymer melts are each different at different temperatures, pointing to an evident breakdown of the TTS. Specifically, we will show that for the same WiR well-entangled polymer melts rupture at relatively low temperatures, yet still 20–30 deg above the glass transition temperature Tg, but undergo necking-like failure at higher temperatures. Thus, at the same WiR, stress–strain curves are significantly different at different temperatures. Moreover, at the lower temperature, these polymer melts can reach an extreme level of extensibility at a critical WiR, which is completely unattainable at higher temperatures. These TTS violating phenomena present a serious challenge to our existing theoretical understanding of nonlinear rheology of entangled polymeric liquids.