On-road operations of Volkswagen light-duty diesel vehicles equipped with defeat devices cause emissions of NOx up to 40 times above emission standards. Higher on-road NOx emissions are a widespread problem not limited to Volkswagen vehicles, but the Volkswagen violations brought this issue under the spotlight. While several studies investigated the health impacts of high NOx emissions, the climatic impacts have not been quantified. Here we show that such diesel cars generate a larger warming on the time scale of several years but a smaller warming on the decadal time scale during actual on-road operations than in vehicle certification tests. The difference in longer-term warming levels, however, depends on underlying driving conditions. Furthermore, in the presence of defeat devices, the climatic advantage of 'clean diesel' cars over gasoline cars, in terms of global-mean temperature change, is in our view not necessarily the case.