The Time-Temperature Superposition (TTS) and Stepped Isothermal Method (SIM) have been implemented to accelerate the creep deformation rate in the tensile creep tests of geosynthetic reinforcement by, respectively, performing a set of tests at different elevated ambient temperatures or stepwise increasing the temperature during sustained loading in a test using a single specimen. Creep strain rates at a fixed reference temperature are estimated by extrapolating those observed at elevated temperatures toward longer elapsed time based on several assumptions validated by a limited amount of experimental data. Any relevant constitutive model that is able to simulate in a systematic way the temperature effects on the load-strain behaviour as observed in the TTS and SIM tests has not been proposed. The stress-strain curves in TTS and SIM tests as well as those from continuous monotonic loading tests at elevated constant temperature are simulated by a constitutive model that takes into account the temperature effects as well as the viscous property. Effects of an increase in the ambient temperature from the reference value to a higher value are modelled by decreasing the stiffness as a result of negative temperature effects on the plastic property (equivalent to negative ageing effects). It is assumed that the elastic and viscous properties are not affected by temperature changes. It is shown that the time history of creep strain and the acceleration of creep strain rate upon an increase in the temperature in TTS and SIM tests can be simulated very well by the proposed model.