The range of an electrically assisted bicycle, which is constrained by the rider's cycling ability and the battery capacity, is heavily influenced by rolling resistance. Furthermore, the magnitude of rolling resistance affects commuters' motivation to decide whether to cycle or to choose another way to commute. This paper presents a way to simulate the transient rolling resistance of bicycle tyres as a function of ambient temperature. The significance of the change in driving resistance at different ambient temperatures is demonstrated through the range simulation of an electrically assisted bicycle at varying ambient temperatures. A representative driving cycle for bicycle commuters was created, enabling comparison of dynamic behaviour in a standardised set, to evaluate the effect of ambient temperature on the battery capacity and the increase in driving resistances. To the authors' knowledge, this kind of model has not previously been created for bicycles. The model calculates tyre temperature based on the heat transfer, considering the heating-i. e., rolling resistance-and cooling effects-i. e., convective and radiative cooling. The decrease in tyre temperature results in an increase in rolling resistance and a decrease in the battery capacity, which was considered in the simulations. The results show significantly increased energy demand at a very low ambient temperature (down to -30 degrees C) compared to + 20 degrees C. The novelty of this article is simulating energy expenditure of bicycle dynamically as a function of ambient temperature. This model includes a temperature-dependent transient bicycle rolling resistance model as well as a battery capacity model. The findings provide researchers with a better comprehension of parameters affecting energy expenditure of bicycles at different ambient or tyre temperatures. The models can be used as a tool during the design process of bicycles to quantify the required battery capacities at different climates. In addition, traffic planners can use the model to assess the effect of changes in infrastructure on motivation to utilise bicycles.