We train convolutional neural networks (CNNs) to predict the distribution of peak warming given the current state of the climate system and varying additional cumulative CO2 emissions. Even if the most ambitious decarbonization goals are achieved, there is >99% probability of exceeding 1.5˚C of long-term global warming, approximately even odds of reaching 2˚C, and high likelihood that the hottest year globally exceeds 2023 by at least 0.5˚C. Further, for more gradual decarbonization that does not reach net-zero CO2 emissions this century, there is >90% probability that the hottest annual global temperature anomaly is twice as large as 2023. The fact that our framework makes highly accurate out-of-sample predictions of the hottest historical year provides confidence in the predicted future probabilities. Given the non-linear sensitivity of many natural and human systems, our results suggest substantial risks from the extreme local conditions that could result from globally hot years during rapid decarbonization.