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Polymers are widely used for lightweight design in industrial applications, such as helmets and car bumpers, where the most common causes of failure or damage are dynamic impact events. It is well known that the mechanical response of most polymers is highly dependent on the loading rate and temperature, and that it is not sufficient to use properties measured under static loads in the analysis of dynamic events. However, the time-temperature equivalence phenomenon offers the chance to predict high-rate performance using low-rate data. In this study, information about the constitutive behaviour of two different molecular weight polycarbonates, is obtained in low-rate experiments and then compared with the high-rate response. A master curve of storage modulus constructed from Dynamic Mechanical Analysis data is employed to understand the viscoelastic response under small-strain loading at various frequencies and temperatures. For the large-strain constitutive response, experiments at strain rates from 0.001 s-1 to 3000 s-1 are performed using a conventional crosshead device, hydraulic device, and split-Hopkinson pressure bar. Moreover, experiments at strain rates of 0.01 s-1 and temperatures from -60 to 120 °C are also performed, and the results are compared. This approach can distinguish ’constitutive’ rate dependence from the effects of specimen self-heating due to adiabatic heating under high-rate deformation. Meanwhile, the molecular weight effects on the mechanical response at varying rates and temperatures are also noted.