This paper considers the financial costs of a rapid national transition to electric vehicles (EVs) in comparison to a baseline scenario that is characterised by continuing use of internal combustion engine vehicles (ICEs). The Australian car fleet, which is responsible for 8% of national greenhouse emissions, is used as a case study. To explore the potential range of costs associated with rapid climate mitigation via the transport sector, the transition is assumed to occur very rapidly (by 2025). The analysis focusses on urban areas, where extensive charging infrastructure is assumed to be made available, including rapid charging facilities. Due to uncertainty over input variables, two “boundary” scenarios were constructed. In the High Cost Scenario, a rapid shift to EVs was found to cost approximately 25% more than the continuing use of ICEs, assessed over the period 2015–2035. However, in the Low Cost Scenario, where costs of EVs (especially batteries) fall more rapidly, EV maintenance costs are at the lower end of projections, and liquid fuel costs at the higher end of projections, a rapid transition to EVs is found to cost approximately the same as the use of ICE vehicles. This suggests that a rapid transition towards EV technologies for urban car travel may offer a cost-effective second-best climate change mitigation strategy. More comprehensive transport sector transformation, including changes in transport and land use policy designed to facilitate mode shift, might further reduce the costs of such a transition.