We investigate committed warming, i.e., the global mean temperature change that would follow complete cessation of anthropogenic emissions. The removal from the atmosphere of short-lived particulate aerosols, which have a cooling effect on the climate, leads to a peak in warming within a decade, followed by a slow decline over centuries to millennia to a relatively stable temperature determined by the residual CO2 forcing. This has important consequences: temporary warming well beyond present-day levels without any additional emissions. We use an emissions-based climate model (FaIR) to estimate temperature change after abrupt cessation of all anthropogenic emissions in 2021 and in every year thereafter until 2080, assuming that emissions prior to cessation proceed along priority Shared Socioeconomic Pathways (SSPs). We find that society may already be committed to peak warming of greater than 1.5°C with approximately 40% probability, with a small (2%) probability of peak warming greater than 2.0°C. The probability of being committed to 1.5°C increases to at least 50% by 2024. Taking into account short-lived climate forcers advances warming commitments by a half a decade, considerably reducing the remaining carbon budget. While an abrupt cessation of all anthropogenic emissions is not likely to occur, this idealized scenario provides a quantification of when we will be committed to exceeding key global warming levels while following realistic emissions scenarios.