The energy consumption of passenger vehicles is affected by the physical properties of the environment. The ambient temperature in particular has a significant impact on the operating energy consumption. To quantify the impact of a changed climate on vehicles with different drivetrain systems, we set up a model that calculates the change in energy demand with respect to multiple global warming levels. In particular, the effect of rising temperatures on the energy consumption of battery electric vehicles and vehicles with internal combustion engines was investigated. Our results indicate that climate change will likely lead to a rise in energy consumption of vehicles with an internal combustion engine. This is mostly due to the increase in cabin climatization needs caused by the higher ambient temperatures. At a global warming level (GWL) of 4.0 °C, the calculated annual energy consumption on average is 2.1% higher than without taking the climate-change-related changes in temperature into account. Battery electric vehicles, on the other hand, are expected to have a lower overall energy consumption (up to −2.4% at 4 °C GWL) in cold and moderate climate zones. They benefit from the lower heating needs during winter caused by global warming.